and Poly2 stacked with Poly1 cantilever beams. The fourth version also had a heater element consisting of Poly1 and Poly2 stacked, but with Poly2 cantilever beams. The fifth and sixth variants featured a modified heater arrangement with Poly1 (fifth version) and Poly2 (sixth version) cantilever beams. Unlike the previous design in which each beam actuated individually, these cantilever beams make contact in sets of 12 when the appropriate potential is applied to the pull-in terminals. This results in trading highly localized passive thermal management for more active control. Electrode structure sizing for pull-in voltage was determine by: (1) where Vp is the pull-in voltage (V), k is a spring force constant (N/m), and is a function of the beam material and dimensions, g is the air gap between the Poly0 electrode and cantilever beam (μm), ε0 is the permittivity of free space (F/m), W is the cantilever beam width (μm), and We is the width of the electrode (μm). The electrode was sized to accommodate a pull-in voltage of approximately 8 V and 12 V, for the variants with Poly2 beams and Poly1 beams, respectively. CAD drawings of the ten layouts were imported into CoventorWare MEMS 2008 for finite element modeling (FEM). Modeling verified the devices structural operation, including correct bimorph cantilever beam curling verses temperature and as-designed electrostatic pull-in voltage. As no provision was made to hermetically seal or package these prototypes, the devices were stored in a nitrogen overpressure drybox within a cleanroom environment. This minimized native oxide growth on the cantilever beam tips and I/O terminal or heat sink sheets – which would have resulted in increased resistivity and thermal contact resistance and thereby decreased prototype performance. 3. Experiment and Results 3.1. Interferometer-based beam displacement testing The mechanical motion of the prototype metamaterial devices is nearly entirely in the Z-axis. For each of the four bimorph cantilever beam array based prototypes, beam displacement verses system temperature was measured. For each of the six electrostatic-actuated cantilever beam array based prototypes, beam pull-in voltage verses system temperature was recorded. System temperature was swept using a calibrated thermoelectric heating/cooling device. Test results for the bimorph cantilever beam array based metamaterials are plotted in Figure 8. Note that this test uniformly heated the entire device. Because of this uniform heating, the temperature at which the array of cantilever beams “closed” is higher than when the devices are heated via Joule heating from the adjacent resistive heating Figure 8. Bimorph cantilever beam tip position verses temperature. When the position equals zero, the beam tip has made contact with the poly layer beneath it. 150 μm beams make contact at 127 °C, 200 μm beams make contact at 123 °C, 250 μm beams make contact at 114 °C, and 300 μm beams make contact at 110 °C. element. When heated via conduction from the heater grid, the gold layer becomes significantly hotter than the polysilicon – resulting in a lower closing temperature than when uniformly heating the device. Measured pull-in voltages for each electrostatic actuated thermal metamaterial variant very closely correlated with the mathematically calculated (using Equation 1) pull-in voltages (8V and 12V). None of the samples evaluated exhibited any temperature dependency in their pull-in performance, and all measurements were within 8% of the calculated pull-in. 3.2. Thermal imaging temperature mapping test In a metamaterial engineered to provide a unique or tailored thermal response, characterization of heat transfer throughout the device is a critical performance metric. An accurate way to evaluate heat transfer on a MEMS-scale device is by using a thermal imaging microscope system. Each of the four bimorph cantilever beam array based prototypes were temperature mapped over the course of an operational sequence. This sequence began with each metamaterial device at a uniform temperature (no power applied to the heater grid). Then, at time T=0 seconds, 24 VDC was applied across the polysilicon resistive heating element, causing ≈ 300 mW of power consumption by the element. Over the next several seconds, the device would heat up, causing the bimorph cantilever beam arrays to bend downwards and close. At approximately T=10 seconds, the device had reached a steady state thermal condition. The potential was then removed from the heater grid – causing the device to rapidly cool and the bimorph beams to curl upwards. Once all 24 of the bimorph beams had recovered to their open position, the operational sequence was complete. 0 5 10 15 20 25 25 35 45 55 65 75 85 95 105 110 115 120 125 130 Beam tip position above I/O terminal or heat sink in μm Device temperature in C 150 μm length beams 200 μm length beams 250 μm length beams 300 μm length beams 111
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