Supporting Information Brown et al. 10.1073/pnas.1311994110 SI Text Model of Thermal Actuation. To explore the characteristics and dependencies of thermal actuation, we developed a simple model to explain the behavior of the system. It is clear that the principal task for any model of this system is to estimate the actuation z of the tip positioned above an active heater (Fig. S2A). To compute this distance, we will use the relation z = L · ΔT · α L ; [S1] where L is the thickness of the polydimethylsiloxane (PDMS), α L is the coefficient of thermal expansion of PDMS, and ΔT is the av- erage temperature change in the PDMS. Therefore, the main task of the model is to compute ΔT, which can be accomplished using a simple lumped element circuit model (Fig. S2B). In this model, the heater is modeled as a constant power supply delivering power P. Because of the high thermal diffusivity of glass relative to that of PDMS, and the much greater thickness of the glass slide (1 mm) vs. the PDMS film (90 μm), heat is assumed to primarily leave the system through the glass. The thermal resistance of the glass slide is modeled as heat diffusing through an infinite half-spherical shell, giving an approximate thermal resistance of R 2 = 1 πDκ glass ; [S2] where D is the diameter of the heater and κ glass is the thermal conductivity of glass. In contrast to the glass slide, which removes heat from the system, the PDMS film is assumed to store heat. The thermal capacity of the PDMS film in the vicinity of the heater is C = πρc P D 2 L 4 ; [S3] where ρ and c P are the density and specific heat of PDMS, re- spectively. For heat to reach the PDMS, it must be conducted through the PDMS, which has a thermal resistance given by R 1 = 2L πD 2 κ PDMS ; [S4] where κ PDMS is the thermal conductivity of PDMS. Now that the model is fully constructed and specified, we can analyze it to gain insight into the physical system measured in Fig. 2 with L = 90 μm and D = 75 μm. Using the following tabulated values for the materials parameters κ PDMS = 0.15 W/m·K, ρ = 970 kg/m 3 , c P = 1,460 J/kg·K (1), and κ GLASS ≈ 1 W/m·K at temperatures between room temperature and 300 °C (2), we find R 1 = 70 kK·s/J, R 2 = 4 kK·s/J, and C = 0.56 μJ/K. This linear system was solved using freely available circuit analysis software (LTspice IV; Linear Tech- nology Corporation) to find calculated heating and cooling curves (Fig. S2C) that qualitatively recapitulate the experimentally mea- sured curves (Fig. 2B). One parameter that can be analytically extracted from this analysis is the heating or cooling time of the thermal capacitor, which is τ = ðR 1 + R 2 ÞC = 41 ms, in excellent agreement with the experimentally measured value of 38 ms. To estimate the scaling of τ with parameters of this system, we ap- proximate τ ≈ R 1 C because R 1 R 2 . In this limit, we find that τ ≈ L 2 2α PDMS ; [S5] where α PDMS = 110 μm 2 /ms is the thermal diffusivity of PDMS (1). Another important parameter that this model can be used to estimate is the actuation efficiency a, which corresponds to the actuation distance per unit applied power P. With regard to the circuit model, this corresponds to the steady-state case when the temperature in the PDMS is constant and the heat steadily flows out through R 1 . The actuation was calculated using Eq. S1 com- bined with the relationship that ΔT = R 2 P, which is the thermal analog to Ohm’s law. Combining these relationships yields a = z P = α L πκ GLASS L D : [S6] Taking α L = 3 × 10 −4 K −1 (3), we compute a = 0.110 μm/mW, in excellent agreement with the measured value of 0.107 μm/mW. It is important to note that this simple model does not account for three aspects of the observed behavior: the biexponential character of the heating and cooling curves, the dependence of rise time on applied power, and the difference between heating and cooling times. However, these effects can be qualitatively understood by considering the temperature-dependent material properties of the system. For instance, thermal expansion of the PDMS film is the purpose of this device, which results in a changing value of L. Because the mass of the PDMS film is not changing during this one-dimensional expansion, the density must be decreasing to compensate, yielding ρðPÞ = ρ 0 L 0 LðPÞ ; [S7] where the subscript 0 denotes the value of the property at ambient temperature. A similar relationship may be written to define the changing PDMS thickness: LðPÞ = L 0 + aP: [S8] Having properties that depend on temperature will lead to non- exponential behavior, because the effective time constant changes as the experiment progresses. To understand why the heating and cooling processes have different time constants, individual exam- ination of these situations is necessary. Considering the case of cooling after the PDMS film is fully actuated, combining Eqs. S7 and S8 with Eq. S5 reveals τ COOL ≈ L 2 0 2α PDMS + aPL 0 2α PDMS ; [S9] which predicts that τ COOL should vary with P with a slope of 0.045 ms/mW, which is commensurate with the experimentally measured value of 0.079 ms/mW (Fig. 2C). This estimate can be further improved by considering more detailed measurements of the temperature variations of the materials properties of PDMS (4). In contrast to the time constant of cooling which increases with applied power, the time constant of heating decreases with applied power. A possible explanation for this phenomenon is revealed by observing the temperature trajectories of the PDMS and heater regions (Fig S2C). As seen experimentally, after power is ap- plied to the system, the temperature in the PDMS (and there- fore the thermal actuation) gradually rises to a maximum value. Brown et al. www.pnas.org/cgi/content/short/1311994110 1 of 7
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Supporting InformationBrown et al. 10.1073/pnas.1311994110SI TextModel of Thermal Actuation. To explore the characteristics anddependencies of thermal actuation, we developed a simple modelto explain the behavior of the system. It is clear that the principaltask for any model of this system is to estimate the actuation z ofthe tip positioned above an active heater (Fig. S2A). To computethis distance, we will use the relation
z=L ·ΔT · αL; [S1]
whereL is the thickness of the polydimethylsiloxane (PDMS), αL isthe coefficient of thermal expansion of PDMS, and ΔT is the av-erage temperature change in the PDMS. Therefore, the main taskof the model is to compute ΔT, which can be accomplished usinga simple lumped element circuit model (Fig. S2B). In this model,the heater is modeled as a constant power supply delivering powerP. Because of the high thermal diffusivity of glass relative to that ofPDMS, and the much greater thickness of the glass slide (1 mm) vs.the PDMS film (90 μm), heat is assumed to primarily leave thesystem through the glass. The thermal resistance of the glass slide ismodeled as heat diffusing through an infinite half-spherical shell,giving an approximate thermal resistance of
R2 =1
πDκglass; [S2]
where D is the diameter of the heater and κglass is the thermalconductivity of glass. In contrast to the glass slide, which removesheat from the system, the PDMS film is assumed to store heat. Thethermal capacity of the PDMS film in the vicinity of the heater is
C=πρcPD2L
4; [S3]
where ρ and cP are the density and specific heat of PDMS, re-spectively. For heat to reach the PDMS, it must be conductedthrough the PDMS, which has a thermal resistance given by
R1 =2L
πD2κPDMS; [S4]
where κPDMS is the thermal conductivity of PDMS. Now that themodel is fully constructed and specified, we can analyze it to gaininsight into the physical system measured in Fig. 2 with L = 90 μmand D = 75 μm. Using the following tabulated values for thematerials parameters κPDMS = 0.15 W/m·K, ρ = 970 kg/m3, cP =1,460 J/kg·K (1), and κGLASS ≈ 1 W/m·K at temperatures betweenroom temperature and 300 °C (2), we find R1 = 70 kK·s/J, R2 = 4kK·s/J, and C = 0.56 μJ/K. This linear system was solved usingfreely available circuit analysis software (LTspice IV; Linear Tech-nology Corporation) to find calculated heating and cooling curves(Fig. S2C) that qualitatively recapitulate the experimentally mea-sured curves (Fig. 2B). One parameter that can be analyticallyextracted from this analysis is the heating or cooling time of thethermal capacitor, which is τ = ðR1 +R2ÞC = 41 ms, in excellentagreement with the experimentally measured value of 38 ms. Toestimate the scaling of τ with parameters of this system, we ap-proximate τ≈R1C because R1 � R2. In this limit, we find that
τ≈L2
2αPDMS; [S5]
where αPDMS = 110 μm2/ms is the thermal diffusivity ofPDMS (1).Another important parameter that this model can be used to
estimate is the actuation efficiency a, which corresponds to theactuation distance per unit applied power P. With regard to thecircuit model, this corresponds to the steady-state case when thetemperature in the PDMS is constant and the heat steadily flowsout through R1. The actuation was calculated using Eq. S1 com-bined with the relationship that ΔT =R2P, which is the thermalanalog to Ohm’s law. Combining these relationships yields
a=zP=
αLπκGLASS
LD: [S6]
Taking αL = 3 × 10−4 K−1 (3), we compute a = 0.110 μm/mW, inexcellent agreement with the measured value of 0.107 μm/mW.It is important tonote that this simplemodel doesnotaccount for
three aspects of the observed behavior: the biexponential characterof the heating and cooling curves, the dependence of rise time onapplied power, and the difference between heating and coolingtimes. However, these effects can be qualitatively understood byconsidering the temperature-dependent material properties of thesystem. For instance, thermal expansion of the PDMS film is thepurpose of this device, which results in a changing value ofL. Because the mass of the PDMS film is not changing during thisone-dimensional expansion, the density must be decreasing tocompensate, yielding
ρðPÞ= ρ0L0
LðPÞ; [S7]
where the subscript 0 denotes the value of the property at ambienttemperature. A similar relationship may be written to define thechanging PDMS thickness:
LðPÞ=L0 + aP: [S8]
Having properties that depend on temperature will lead to non-exponential behavior, because the effective time constant changesas the experiment progresses. To understand why the heating andcooling processes have different time constants, individual exam-ination of these situations is necessary. Considering the case ofcooling after the PDMS film is fully actuated, combining Eqs.S7 and S8 with Eq. S5 reveals
τCOOL ≈L20
2αPDMS+
aPL0
2αPDMS; [S9]
which predicts that τCOOL should vary with P with a slope of0.045 ms/mW, which is commensurate with the experimentallymeasured value of 0.079 ms/mW (Fig. 2C). This estimate can befurther improved by considering more detailed measurementsof the temperature variations of the materials properties ofPDMS (4).In contrast to the time constant of cooling which increases with
applied power, the time constant of heating decreases with appliedpower. A possible explanation for this phenomenon is revealed byobserving the temperature trajectories of the PDMS and heaterregions (Fig S2C). As seen experimentally, after power is ap-plied to the system, the temperature in the PDMS (and there-fore the thermal actuation) gradually rises to a maximum value.
Brown et al. www.pnas.org/cgi/content/short/1311994110 1 of 7
In contrast, the temperature of the heater (considered in thismodel to be the node in between the resistors corresponding to thePDMS and glass) rises immediately to 90% of its maximum value.Because the thermal conductivity of the glass depends strongly ontemperature (5), this drastic difference in local temperature be-tween the heating and cooling curves could have a large impact onR2, lowering τHEAT but not affecting τCOOL.
Estimation of Maximum Actuation. When no power was appliedto the heaters, imaging with a thermal camera (SC7000; FLIRSystems) exposed the structure of the leads and coils as slightdifferences in temperature (Fig. S3A, Upper). When 28 mW wasapplied to the top left heater for 1 s, a temperature plumecentered on the selected heater is visible (Fig. S3A, Lower).The way in which the resistance changes with applied power can
provide information about the local temperature of the resistiveheaters. As both the current and voltage were measured in typicalactuation experiments (Fig. 2) the resistance was also calculated ateach applied power (Fig. S3B). The resistance linearly increasedfrom the dc value of 2.913 kΩ as the applied power increased,consistent with the positive temperature coefficient of resistance(TCR) of a normal conductor. The TCR of these indium tin oxide(ITO) heaters was found by measuring the resistance of an ITOheater while it sat on the heated stage of a probe station (ST-500;Janus Research Company) and was found to be 570 ± 40 ppm/°C.There was also series resistance from the leads that did notchange temperature during the measurement, which was mea-sured to be 700Ω. Combining these data allowed us to convert theresistance changes (Fig. S3B) to measurements of the tempera-ture of the heater (Fig. S3C). A linear fit to this data reveals theheating efficiency of this device to be 11.3 ± 0.2 °C/mW. BecausePDMS begins to thermally decompose (6) between 500 and 600 °C,taking 400 °C (ΔT = 380 °C) to be an estimate of a safe maximumtemperature led to an estimated maximum delivered power of34 mW, or 43 mW of applied power, resulting in a maximumactuation distance of 4.6 μm for this device.
Measurement of Cross-talk and Fatigue.We evaluated the cross-talkand degradation associated with thermal actuation. Atomic forcemicroscope measurements were taken at positions along thesurface of the PDMS to map the actuation amplitude vs. distancefrom a heater to which 28 mW was periodically applied (Fig. 2D).Furthermore, the amplitude profile was recorded at differenttimes after the beginning of a 1-s power pulse (Fig. S4A). In-terestingly, τ varies linearly with distance from the active heaterdue to the increased distance that heat must diffuse (Fig. S4A).This is an important result because it implies that by tuning theduration of the applied power, one can control the horizontalextent of actuation. For example, when the power is applied for50 ms, the actuation magnitude at a distance of 150 μm from theactive pen is only 21% of the actuation magnitude of the selectedpen (Fig. 2D), thereby minimizing cross-talk. To investigatewhether heating PDMS in this way affects its properties, thissample was subjected to a fatigue test in which the heater was
cycled 23,000 times over 12 h and then the actuation profile wasmeasured again, resulting in nearly indistinguishable performance(Fig. 2D).
Patterning Apparatus. Finished active PPL pen arrays weremounted on a custom printed circuit board (Fig. S6A) with silverepoxy (CW2460-ND; Digi-Key Corporation) and attached to thez-piezo of a commercial scanning probe lithography instrument(XE-150; Park Systems) (Fig. S6B). The motions of this instru-ment were controlled by a computer running commercial soft-ware (Fig. S7A). The current applied to each heater in the penarray was controlled by custom electronics wherein the ground ofeach heater was wired to an NPN transistor that was toggled bydigital output lines from a National Instruments data acquisitionsystem (NI-DAQ USB 6212). The supply power to the entirearray was provided by a dc power supply (1651A; B&K PrecisionCorp.) and the duty cycle was modulated by a clock channel onthe NI-DAQ to provide software control over the power used toactuate each pen. The state of the NI-DAQ was controlled bycustom software written in MATLAB (The MathWorks, Inc.).Additionally, the NI-DAQ was used to monitor the z-position ofthe tip array by measuring the voltage produced by the strainsensor of the scanning probe instrument.Before writing a pattern, the tip array must be leveled with
respect to the patterning surface and any piezostage–array mis-alignment must be compensated for by using a plane correctiontechnique. First, the tip array was moved toward the sample untilsome of the tips visibly deform. Next, the stage was tilted se-quentially along the y and x axes such that all probes came intocontact (observed as deformation of the tips) with the surface atthe same z-piezo extension. Next, to compensate for misalignmentbetween the piezostage and the tip array, the tip array was movedto the four corners of the 150 × 150 μm2 patterning region and thez-piezo extension that resulted in contact with the surface wasrecorded. A plane was fit to these four (x, y, z) coordinates todefine the contact plane between the tips and the substrate. Thisplane was stored in software as a calibration.In a typical patterning experiment, an arbitrary image was
reproduced onto a sample through the coordinated actions of theactuator array and the scanning probe lithography platform. Thepatterning proceeds as follows. (i) The desired image was loadedinto custom software on the MATLAB computer, which de-composes the image into 16 frames according to what each penwill write. Using this information, the MATLAB software gen-erated a .ppl file that contains instructions for the Park Systemssoftware to sequentially move the pen array around the pat-terning substrate. (ii) The Park Systems software moves the tiparray to the first patterning position. (iii) Having detected themotion of the tip array, the MATLAB software steps through thepens that should write at that location by setting the duty cycle forthat pen, and then actuating the transistor controlling that heaterfor a specified amount of time. (iv) Steps ii and iii are repeateduntil the pattern is completely written.
1. Mark J (1999) Polymer Data Handbook (Oxford Univ Press, New York).2. Haynes WM, ed (2012) CRC Handbook of Chemistry and Physics (CRC, Boca Raton, FL),
sensors based on the thermal expansion of transparent elastomeric media. Rev SciInstrum 70(4):2031–2037.
4. Kline DE (1961) Thermal conductivity studies of polymers. J Polym Sci, Polym Phys Ed50(154):441–450.
5. Powell RW, Ho CY, Liley PE (1966) Thermal conductivity of selected materials. NationalStandard Reference Data Series (National Bureau of Standards, Washington, DC).
Fig. S1. Fabrication procedure used for active polymer pen lithography pen arrays.
Fig. S2. Model of thermal actuation. (A) Schematic of the geometry of a single active pen. (B) Circuit diagram that describes the thermal behavior of an activepen. (C) Simulated current and temperature profiles from the model shown in B.
Brown et al. www.pnas.org/cgi/content/short/1311994110 3 of 7
Fig. S3. Thermal measurements of actuation. (A) Infrared thermographs showing the tip array in the quiescent state (Upper) and when the top left pen hasbeen powered with 28 mW for 1 s (Lower). (B) Measured resistance of the heater coil at different values of applied power. (C) Estimated temperature changeon the tip array as a function of the power delivered to the heater coil.
Fig. S4. Measurement of cross-talk. (A) Actuation profiles at different times after heating. Actuation at neighboring pens (located at X = 150 μm) is mitigatedby operating at shorter actuation times. (B) Rise time as a function of distance from the active pen. Once beyond the edge of the heater, the rise time grows ata rate of 0.6 ms/μm. This illustrates why short actuation times do not actuate nearby pens.
Brown et al. www.pnas.org/cgi/content/short/1311994110 4 of 7
Fig. S5. Nonidealities of patterning with a 2D array of probes. The left column schematically represents the issue and the right column represents themanifestation of the problem in the pattern generated by 2 × 2 probes.
Fig. S6. Active polymer pen lithography (PPL) apparatus. Photographs of (A) the printed circuit board (PCB) on which an active PPL pen array (transparentglass in the center) is mounted and (B) the PCB mounted in the scanning probe lithography instrument.
Brown et al. www.pnas.org/cgi/content/short/1311994110 5 of 7
Fig. S7. Diagrams of the experimental apparatus. (A) Circuit diagram of the control circuitry used to supply variable power to each pen in the active PPL penarray. (B) Block diagram of the experimental apparatus.
Fig. S8. Patterning with 100-nm pitch. (A) SEM image of a pattern written by one pen in an active PPL array in which the applied power is varied from 0 to10 mW as the pen writes copies of five dots with a pitch of 100 nm. In this experiment, the actuation time is 500 ms and the relative humidity is 60%. Asexpected, when the power is just sufficient for the pen to make contact with the surface (Upper Right), the dots are resolvable as discrete features. (B) Thethree features written under this condition. Two features are missing from this series because for those points the applied power was not sufficient for the pento make contact with the surface. As the power increases, the features become increasingly large and begin to overlap. Because each pattern has 200 points,the effective difference in extension between each point in this array is ∼2.5 nm. This experiment shows that with sufficient control over the tip-sampleseparation, writing features at 250,000 dots per inch is possible.
Brown et al. www.pnas.org/cgi/content/short/1311994110 6 of 7
Movie S1. Real-time optical movie depicting the thermal actuation of a 4 × 4 pen array. The movie shows many cycles of each of the 16 probes being actuatedsequentially for 100 ms. The pen-to-pen pitch is 150 μm.
Movie S1
Brown et al. www.pnas.org/cgi/content/short/1311994110 7 of 7
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