ABSTRACT
Metamaterials are engineered materials with integrated structures designed to produce a resonant response at specific frequencies. The capacitive and inductive properties of metamaterials effect the overall refractive index of the media in which an RF signal propagates by generating a resonant frequency response. Incorporating microelectromechanical systems (MEMS) into the structure adds the ability to tune metamaterials and generate a variable resonance. In this investigation, a resonant response is achieved for the 1 -4 GHz range with tuning. Employing processing techniques to create microelectronic devices, different metamaterial designs are fabricated on quartz substrates. Using these modifications, a design which provides the ideal shift in resonance is selected to incorporate into future RF systems. This paper reports on the modeling, design, fabrication and testing of various designs of metamaterials incorporated with MEMS.
Keywords: Metamaterials, Split Ring Resonator, MEMS
INTRODUCTION
Metamaterials ability to induce a negative refractive index at certain frequencies has gained attention within the last decade. The research covers areas of the electromagnetic spectrum from acoustic to optical frequencies. Metamaterial research began with Pendry’s postulation that the split ring resonator (SRR) could be used to create an effective negative permeability [1]. This concept was first verified by Smith et al. [2] and the SRR has since become a staple in metamaterial designs [3-9]. The resonant frequency of the SRR depends on the structure dimensions, material composition, and frequency of the incident radiation. The design of the SRR structure will determine the capacitance and inductance which define the resonant frequency [4]. The permittivity of the host material used to fabricate the SRR will also affect the resonance. However, the resonance and therefore the region in which the structure will exhibit a negative permeability, generally covers a narrow portion of the electromagnetic spectrum. Developing a method to tune the resonant frequency is desirable for extending the range of negative permeability. Through this research, variable resonance of split ring resonators is realized by incorporating microelectromechanical systems (MEMS) cantilever arrays into the SRR design to varying the overall capacitance and in-turn adjusting the resonance frequency.
DESIGN
Combining the MEMS cantilevers with the baseline SRR offers a unique way to create variable resonance from an otherwise static design. Incorporating MEMS into the SRR structure brings functional mechanical capabilities to the designs at the micro-level which is essential for varying capacitance of the small structures.
A SRR without cantilevers was modeled, fabricated, and tested to verify the design process and use as a reference. The SRR design along with the voltage and ground traces is shown in Figure 1a. The unit cell includes the SRR along with the voltage and ground traces. The traces are also affected by the electromagnetic field which induces low frequency plasma on the traces. The baseline SRR was arranged in a 1 x 4 periodic array for RF testing to establish the base resonant frequency of the modified designs. The RF transmission spectrum is shown in Figure 1b. The spectrum shows a narrow resonance at 2.83 GHz and the transmission drops to zero. The off resonance transmission is 100%. The reference split ring resonator aids in determining the inductance and capacitance parameters inherent to the structural design and material composition that establish the resonant frequency.
Figure 1 (a) Diagram of the baseline SRR with additional traces, and(b) the RF transmission spectrum showing resonance at 2.83 GHz
The model of the baseline SRR is used to determine the initial dimensions of the design to create a resonance at the desired frequency. From this design, the requirements necessary to change the capacitance of the structure to smoothly shift the resonant frequency are identified. The analytical model for the resonant frequency is given below,
where LOuter is the inductance of the outer resonator ring, LInner is the inductance of the inner resonator ring, COuter is the capacitance for the outer resonator ring, CInner is capacitance of the inner resonator ring, CLeftTrace is the capacitance for the left trace, CRight Trace is the capacitance for the right trace.
Two design options were used to vary the capacitance of the SRRs. The first option incorporates cantilevers in the gap of the SRR that are actuated through electrostatic force and will increase the gap capacitance. The second option utilizes the cantilevers to increase the capacitance between the inner and outer ring by connecting them as the cantilevers are actuated.
The first design, shown in Figure 2a, integrates cantilevers into the gaps of both the inner and outer resonator rings. The cantilever array consists of five cantilevers 300 ^m wide that vary in length. The length of each cantilever varies by 50 ^m to have beam lengths ranging from 300 to 500 ^m. Each beam tip extends over the gap to opposite side of the SRR overlapping the SRR by 75 ^m. The cantilever is isolated from the SRR by a 0.3 ^m layer of silicon nitride. The cantilever has a gap height of 2.0 ^m. The actuation pad under each cantilever is shifted to vary the pull-in voltages. The pull-in voltage is calculated with
where z0 is the initial gap height, km is the material spring constant, and C0 is the capacitance of the cantilever at the initial gap [10]. The dominating parameter for the pull-in voltage is the spring constant km defined as
where E is the Young’s Modulus, w is the cantilever width, t is cantilever thickness, and l is the cantilever length. From Equation (3), it can be seen that the cantilever thickness and length determine the pull-in voltage. The cantilever thickness will be varied to determine the ideal thickness for minimizing the stress in the electroplated layer. The capacitance each cantilever contributes is based on the area that it comes into contact with the SRR. For these cantilevers, the area is 300 x 75 pm. As each beam pulls in, it contributes approximately 0.6 pF to the overall capacitance.
The next design modification incorporates cantilevers between the inner and outer resonator rings, as shown in Figure 2b. Four cantilevers make up a set of variable capacitors for the design which is laid out around the resonator rings in four locations. There are two sets of cantilever arrays located on the adjacent sides of the SRR from the gap. For this design, the cantilever arrays consist of 4 beams each 300 pm wide, whose length varies from 350 to 500 pm in 50 pm steps. The beams extend from the inner SRR across the gap to the outer resonator ring, overlapping the outer SRR by 75 pm. The actuation pads are placed between the rings at locations to vary the pull-in voltage. The longest beams on all four arrays should pull-in at the same voltage, thus creating four shifts in the resonant frequency.
The third design modification, shown in Figure 2c, places cantilevers in the SRR gaps as well as in between the resonator rings. The cantilever arrays in this design have the same dimensions as those of the first and second design. The overall intention of this design is to increase the range in which the resonance frequency shifts by incorporating more cantilevers for a larger increase in the capacitance. With all the cantilevers at the same length having the same pull-in voltage, the design has a larger shift in resonance per cantilever.
Figure 2d is a diagram of the fourth design. In this design, three cantilever arrays consisting of four beams were placed in between the resonator rings. The widths of each cantilever array are varied to change the capacitance area of each array. One set of the cantilevers has a width of 300 pm while the other cantilevers sets are 400 and 500 pm wide. Increasing the area creates a broader change in capacitance than the other designs.
Developing the modified structures from the baseline design presented some design challenges. For instance, the actuation pads and interconnects add unnecessary capacitance and inductance which shifts the resonant frequency. To alleviate this problem, the interconnects are scaled to smaller sizes to minimize the additional capacitance and/or mutual inductance.
In the modified designs, the metal components are fabricated with gold to improve: conductivity, ease of micro fabrication, and prevent oxidation of the material. A quartz substrate was used as a base for the metal components to increase electrical isolation [10]. All four different designs were fabricated based on the two modification options in order to test the effect of integrating MEMS cantilevers into the SRR structure and determine the configuration that offered the widest tunable range.
Figure 2 Layouts of the four design variations integrated with (a) cantilevers in the gap, (b) cantilevers between rings, (c) cantilevers in the gap and connecting the rings, and (d) cantilevers with varying widths between the rings
MODELING
CoventorWare, a design and simulation suite for all phases of MEMS production, was used to simulate the designs created by Coventor Inc [11]. CoventorWare performs finite element modeling and boundary element modeling to simulate the functionality of the MEM cantilevers used for each SRR design. The CoventorWare Analyzer provides a method to simulate electrical and mechanical response of MEMS. The simulation tests for: capacitance, inductance, temperature, resistance, current density, pull-in voltage, and release voltage of the cantilevers. Using CoventorWare to optimize the design before fabrication saves time and material.
All four designs were modeled with CoventorWare at 0 VDC to determine the initial capacitance and inductance of each design so that the starting resonance frequency could be calculated. Figure 3 is a CoventorWare diagram of Design 1 with insets showing the cantilevers up and again with an applied voltage to actuate the longest cantilever. The CoSolveEM Analyzer was used to simulate the capacitance for the design with all the beams in the initial state. The inner and outer ring capacitance is 0.668 and 1.301 pF, respectively. The left and right trace capacitance is 0.269 and 0.518 pF, respectively. The other designs were simulated with CoventorWare at 0VDC obtaining the values given in Table 1.
The inductance for the designs is simulated using the MEMHenry Analyzer. Inductance values calculated for the inner and outer resonator ring for Design 1 are 9.295 and 18 nH, respectively. The capacitance and inductance values along with Equation (1) were used to calculate a resonant frequency of 2.06 GHz for Design 1. Table 1 lists the capacitance, inductance, and resonant frequency for all four design layouts.
Figure 3 CoventorWare diagram of Design 1, an SRR with cantilevers in the gap. The insets show the cantilevers in a) the initial state and b) a state with the longest beam pulled-in
Table 1 Simulated capacitance and induction parameters of the different designs at 0 VDC; along with the calculated resonant frequency for each design
 |
 |
 |
 |
 |
 |
 |
 |
|
1 |
18 |
9.295 |
1.301 |
0.668 |
0.269 |
0.518 |
2.06 |
|
2 |
18 |
9.295 |
1.478 |
1.136 |
0.271 |
0.312 |
1.91 |
|
3 |
18 |
9.295 |
1.877 |
1.338 |
0.251 |
0.304 |
1.76 |
|
4 |
18 |
9.295 |
2.53 |
1.947 |
0.321 |
0.277 |
1.53 |
TESTING
Device characterization is performed on the SRR array and test devices of cantilevers. Characterization is performed in two phases. Phase one characterization consists of testing the cantilevers for DC voltage response by applying voltage to the actuation pads. The DC testing is conducted with a DC power supply, multimeter, and a Zygo white light interferometer. The Zygo instrument helps to inspect the cantilevers while stepping up the DC voltage on the actuation pads. This method of testing helps determine the pull-in voltages of the design and provides a quick method to inspect the actuation of the cantilevers. By completing the DC testing, the test results can be compared to the simulation and see how well results obtained from the modeling analysis fit for the cantilevers. Figure 4 shows an image obtained with the Zygo instrument while applying 15 VDC to the actuation pads which caused the longest cantilever to pull-in.
Figure 4 Cantilevers from Design 1 with the 500 pm cantilever pulled-in. Image obtained with the Zygo while applying 15 VDC to actuation pads through the DC traces
Phase two characterization consists of RF testing on the SRR arrays and test devices. The test devices were used to test how each cantilever set contributes to the change in capacitance. The test devices also serve in process development of the fabrication steps. The SRR arrays were tested using a 4 GHz strip-line and Agilent Programmable Network Analyzer (PNA). Figure 5 shows Design 1 inserted in the strip-line for testing. In order to test the samples, the PNA was calibrated with the 4 GHz strip-line and shorting straps. The calibration ensures the measured RF spectrum from 10 MHz to 4 GHz have low signal noise and reduces any attenuation. After completing the calibration, the samples are inserted in the strip-line and measured at 0 VDC up to the voltage necessary to pull-in all the cantilevers. The measurements are analyzed to determine which SRR design provided the greatest variation of the resonance response.
Figure 5 Experimental setup showing 4 unit cells of Design 1 in the strip-line with the DC wires bonded to the actuation pads. The array is suspended between the inner conductor and outer conductor by Styrofoam.
RESULTS
Each design was thoroughly tested to ensure the functionality of the cantilevers as well as to identify the initial resonant frequency and the shift in the resonance due to the cantilever actuation. The cantilevers on each layout performed in a uniform manner; they actuated one at a time, longest to shortest, and within the calculated range for the pull-in voltage. The RF measurements on the other hand produced varying results for each of the four layouts.
The transmission results for Design 1 (cantilevers in the SRR gap region) with an applied voltage of zero to 20 Volts are shown in Figure 6. This layout has an initial resonance at 2.06 GHz, matching the resonance calculated using the capacitance and inductance from the CoventorWare simulations. Applying the DC actuation voltage caused the resonant frequency to shift to lower frequencies as expected. At the applied 20 VDC, the resonance frequency is 1.88 GHz, for an overall shift of 0.18 GHz. The CoventorWare simulations predicted an overall shift of 0.27 GHz for this design. This discrepancy could be due to the lack of uniformity in the cantilevers at pull-in which can cause the SRRs not to produce an identical capacitance.
Figure 6 Transmission results of Design 1 obtained from strip-line measurements
Design 2, the cantilevers connecting the inner and outer SRRs, has an initial resonance of 1.92 GHz. This resonance is in good agreement with that calculated with Equation1. Figure 7 shows the transmission spectrum design of Design 2 plotted as a function of the actuation voltage. The sample has a thicker electroplated gold layer which resulted in much higher pull-in voltages to actuate the beams. The applied DC actuation voltage only created a minor shift in the resonance. The simulation predicted a much larger tuning effect from this design. The differences between the measurements and the simulations could be a result of the gap spacing for the cantilevers not being uniform. This would affect the overlap area and gap spacing of the cantilevers and the SRR significantly reducing the added capacitance of each cantilever.
The transmission spectra for the third and fourth designs did not have a resonant frequency. Design 3 (cantilevers in both the SRR gaps and inner ring spacing) had a predicted initial resonance of 1.76 GHz based on the simulation. Even though a resonance was not observed, a voltage was applied to actuate cantilevers to look for any type of signal disturbance.
Similar to Design 3, the fourth design (cantilevers with varying widths connecting the SRR rings) also did not display an initial resonance at the calculated value of 1.5 GHz, or within the frequency range measured. The transmission was not disturbed nor could any resonance shift be observed as the applied voltage was increased.
Figure 7 Transmission data measured for Design 2 showing resonance at 1.92 GHz but shifting only 0.04 GHz as the voltage is increased from 0 to 110 VDC. The cantilever thickness was increased to 5.0 pm which increases the pull-in voltage.
CONCLUSION
The SRR has a static resonant response based on the material composition, geometric layout, and type of propagating signal. Adapting the baseline SRR design with cantilevers provides a method to tune the resonant response by changing the capacitance associated with the SRR. Conducting research on the four designs provided valuable information about the design method, modeling, fabrication and testing of the modified SRRs. From these results, Design 1 is chosen for the fabrication of a bulk array to test the structure within a focused beam system and observe the two dimensional effects of a bulk SRR system integrated with cantilevers.
