Resonant frequency of gold/polycarbonate hybrid nano resonators fabricated on plastics via nano-transfer printing
© Dechaumphai et al; licensee Springer. 2011
Received: 15 September 2010
Accepted: 17 January 2011
Published: 17 January 2011
We report the fabrication of gold/polycarbonate (Au/PC) hybrid nano resonators on plastic substrates through a nano-transfer printing (nTP) technique, and the parametric studies of the resonant frequency of the resulting hybrid nano resonators. nTP is a nanofabrication technique that involves an assembly process by which a printable layer can be transferred from a transfer substrate to a device substrate. In this article, we applied nTP to fabricate Au/PC hybrid nano resonators on a PC substrate. When an AC voltage is applied, the nano resonator can be mechanically excited when the AC frequency reaches the resonant frequency of the nano resonator. We then performed systematic parametric studies to identify the parameters that govern the resonant frequency of the nano resonators, using finite element method. The quantitative results for a wide range of materials and geometries offer vital guidance to design hybrid nano resonators with a tunable resonant frequency in a range of more than three orders of magnitude (e.g., 10 KHz-100 MHz). Such nano resonators could find their potential applications in nano electromechanical devices. Fabricating hybrid nano resonators via nTP further demonstrates nTP as a potential fabrication technique to enable a low-cost and scalable roll-to-roll printing process of nanodevices.
Flexible electronics is an emerging technology that will have a significant social impact through an exciting array of applications, such as low-cost electronic paper, printable thin-film solar cells, and wearable power harnessing devices, to name a few [1–7]. Future success of flexible electronics hinges upon new choices for fabrication processes that are cost-effective, scalable to large areas, and compatible with both organic and inorganic materials . Roll-to-roll printing of flexible devices allows for dramatic reduction in capital and device costs, resulting in lightweight, thin, rugged, and large area flexible devices . While this promising technology still being in its infancy, there are existing efforts to explore enabling printing technology for roll-to-roll process, such as ink-jet printing , micro-contact printing (μCP) [11, 12], and nano-transfer printing (nTP) [13–19]. Unlike inkjet printing and μCP, nTP is inherently compatible with nano-scale features and the resulting devices are as good as those fabricated via traditional processing methods . nTP primarily relies on differential adhesion for the transfer of a printable layer from the transfer substrate to a device substrate. Various organics and inorganics can be printed in the same manner thus avoiding mixed processing methods and allowing multilayer registration. So far, nTP has been successfully used to fabricate a range of functional components for flexible devices, such as organic thin-film transistors (OTFTs) , carbon nanotube TFTs , graphene TFTs [16, 21], and inductors. In this article, we report the fabrication of gold/polycarbonate (Au/PC) hybrid mechanical nano resonators on plastic substrates through an nTP process, and the parametric study of the resonant frequency of the resulting hybrid nano resonators.
A 200-500-nm-thick Au printable layer was fabricated on a Si transfer substrate using standard photolithography, followed by metals deposition using an e-beam deposition system and lift-off. The resulting Au pattern was used as an etch mask such that the Si transfer substrate was etched to a depth of approximately 8 μm in an RIE chamber using 20 SCCM SF6, 20 mTorr, and 100 W. The Au printable layer covering the raised portion of the templated transfer substrate was printed onto a PC device substrate in a Nanonex NX2500 nano-imprintor at 160°C and 500 psi for 3 min. A second transfer substrate was prepared by performing metals deposition of a 35-nm Au film through a shadow mask onto a Si transfer substrate and then spin coating a 200-nm thick PC film over the Au film. The Au/PC membrane was transfer printing over the previously printed PC substrate at 130°C and 500 psi for 3 min. Note that the first printing temperature is above the glass transition temperature (T g) of the PC substrate while the second printing temperature is below T g. The higher temperature was used to ensure that the templated surface was fully replicated into the surface of the PC substrate while the lower temperature was used to ensure that the templated surface of the PC substrate was retained. The resulting mechanical resonator is shown in Figure 3a. Note that this device exhibits wrinkles in the top layer Au/PC membrane. Such features result from the compressive strain built up within the Au membrane due to the differential thermal expansion between the Au and PC materials. Figure 3b shows a similar device where the Au membrane was deposited near room temperature in an e-beam evaporator rather than transfer printed at 130°C. Note that the device containing the directly deposited Au film has notable fewer wrinkles than the device containing the printed Au film.
A preliminary measurement of the resonant frequency on these devices was performed visually under an optical microscope. The top and bottom electrodes were contacted using probe tips connected to a square wave AC voltage source. A voltage of approximately 100 V was applied across the electrodes as a means to mechanically excite the devices and the frequency swept from 400 to 600 KHz for the device in Figure 3a and from 10 to 35 KHz for the device in Figure 3b. The optical microscope was initially in focus on the surface of the Au/PC film. As the frequency of the applied voltage reaches the resonant frequency of the nano resonator, the Au/PC film is exited and starts to vibrate. As a result, the surface of the Au/PC film in the microscope becomes out of focus. The frequency as a change in focus of the Au/PC film surface was recorded as the resonate frequency. In this way, the resonant frequencies were estimated to be 520 and 25 KHz, respectively. It is expected that the resonant frequency of a hybrid nano resonator depends on both the geometric parameters of the design (i.e., the width of the cavity over which Au/PC is fabricated, the thickness of the Au/PC film) and the mechanical properties of the constituent materials (i.e., elastic moduli of Au and PC). For example, a similar nano resonator fabricated over a narrower cavity has a higher resonant frequency, with all other parameters remaining the same.
To guide further experiments and explore the design limit of hybrid nano resonators fabricated via nTP, we next perform systematic parametric studies to investigate the effects of aforementioned governing parameters on the resonant frequencies of hybrid nano resonators, using finite element analysis. Specifically, we study the effects of the PC thickness, the cavity width, and the elastic modulus of the polymeric film (e.g., if a polymer different from PC is used). The results from the parametric studies can serve as guidelines to design hybrid nano resonators with tunable resonant frequencies.
Material properties used in computational model
Elastic modulus (GPa)
19.3 × 103
1.2 × 103
In the parametric studies, we fixed the thickness and the elastic modulus of the Au film to be 35 nm and 78 GPa, respectively. The thickness of the polymeric film H was varied between 0.2 and 10 μm and the elastic modulus of the polymeric film E was varied between 10 MPa and 10 GPa (e.g., corresponding to a range from a compliant elastomer film to a stiff plastic film). The cavity width d is varied between 5 and 50 μm. The resonant frequency analysis was carried out via eigenmode and eigenvalue extraction using Lanzcos method in ABAQUS 6.9.
In our parametric studies, our simulation models correspond to a hybrid nano resonator fabricated over an infinitely long cavity. Compared to that fabricated over a square cavity (e.g., Figure 3), our simulation model ignores the mechanical constraint imposed by another two sides of the cavity to the Au/PC bilayer. In this sense, our simulation results underestimate the resonant frequencies of nano resonators fabricated in our experiments. For example, the predicted base mode resonant frequency is 119 KHz for H = 0.2 μm and d = 50 μm, which falls in between the two measured resonant frequencies (520 and 25 KHz, respectively). Further measurement of the resonant frequencies of the hybrid nano resonators at higher precision is under exploration and will be reported elsewhere. In our simulations, the wrinkles in the Au films due to thermal mismatch during nTP process are not considered. Wrinkles in the Au film lead to increased bending resistance of the nano resonator, therefore result in a resonant frequency higher than that of a smooth nano resonator. In this sense, the simulation results underestimate the resonant frequency of the Au/PC nano resonators. Recent study shows that the interfacial defects also affect the quality of nTP process . For example, an interfacial delamination along the interface between transfer substrate and printable layer (Figure 1) is beneficial, while that along the interface between printable layer and device substrate is detrimental for the success of nTP process. Such understandings can be indeed leveraged to enhance the quality of nTP processes, such as by introducing pre-delamination along the desirable interface via controlled adhesion. We will explore such a strategy in future works to further improve the yield of the nano resonator fabrication.
In summary, we fabricated Au/PC hybrid mechanical nano resonators on plastic substrates through an nTP process, and conducted systematic computational studies to decipher the geometric parameters and mechanical properties that govern the resonant frequency of the resulting hybrid nano resonators. We showed that the hybrid nano resonators can be mechanically excited when the frequency of the applied AC voltage reaches the resonant frequency of the hybrid nano resonators. The quantitative results for a wide range of materials (from PC to elastomers) and geometries offer vital guidance to design hybrid nano resonators with a tunable resonant frequency in a range of more than three orders of magnitude (e.g., 10 KHz-100 MHz). Given the versatility of nTP process, it is reasonable to expect that such designs of nano-scale resonators can be achieved. While the exploration reported in this article is still preliminary, there is no doubt that such hybrid nano resonators could find their potential applications in nano- electromechanical devices. Fabricating hybrid nano resonators via nTP further demonstrates nTP as a potential fabrication technique to enable a low-cost and scalable roll-to-roll printing process of nanodevices.
organic thin-film transistors.
The authors are indebted to Daniel R. Hines for his invaluable help in sample preparation and nTP process. TL acknowledges the support of NSF under Grant #0928278. ZZ thanks the support of A. J. Clark Fellowship, and UMD Clark School Future Faculty Program.
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