A miniature MEMS switch is designed, fabricated, and incorporated in a reconfigurable metallic mesh filter for broadband terahertz modulation. The mechanical, electrical, and geometrical properties of the MEMS switch are set to enable broadband terahertz modulation with relatively low modulation voltage, high modulation speed, and high device reliability. The implemented miniature MEMS switch exhibits an actuation voltage of 30 V, a fundamental mechanical resonance frequency of 272 kHz, and an actuation time of 1.23 μs, enabling terahertz modulation with a record high modulation depth of more than 70% over a terahertz band of 0.1-1.5 THz, with a modulation voltage of 30 V and modulation speeds exceeding 20 kHz.
© 2014 Optical Society of America
The capability of micro-electro-mechanical devices to allow on-chip mechanical movements has offered a unique platform for developing advanced sensors and reconfigurable electronics/optoelectronics. It has enabled the development of high-performance pressure sensors , accelerometers , gyroscopes , microfluidic valves , projection displays , tunable lasers , and a wide range of reconfigurable electronic circuits and systems [7, 8]. This capability is also of great importance for developing high performance terahertz modulators since existing optical modulation methods [9–17] are limited by the lack of materials with the desired properties and practical challenges in scaling device dimensions to operate efficiently in the terahertz regime. As a promising solution, artificial materials with high terahertz wave transmission can be engineered by arranging specifically-designed subwavelength structures in a two-dimensional or three-dimensional array. Subsequently, terahertz wave transmission can be significantly reduced by mechanical reconfiguration of the structure that modifies its electromagnetic properties. Compared to other terahertz modulators based on reconfigurable metamaterials with optical, magnetic, and thermal control, terahertz modulators based on MEMS-reconfigurable metamaterials have the great advantage of offering a fully integrated solution through a voltage-controlled and room-temperature device platform.
On the basis of this promising solution, a number of terahertz modulators based on MEMS-reconfigurable metamaterials have been demonstrated [18–22]. However, the bandwidth of the demonstrated terahertz modulators based on MEMS-reconfigurable metamaterials has been limited by the resonance nature of the utilized metamaterial structures. To address this limitation and achieve the broad modulation bandwidth required in time-domain and frequency-tunable terahertz spectroscopy and imaging systems, reconfigurable meta-surfaces with double-layered metallic mesh filters have been proposed [Fig. 1] [23–25]. Each individual mesh filter consists of a periodic arrangement of metallic patches [Figs. 1(a) and 1(b)] or metallic slits [Figs. 1(b) and 1(c)] integrated with MEMS switches. Before actuating the MEMS switches, the two mesh filters are separated from each other, exhibiting capacitive (low-pass filter) behavior in response to an incident electromagnetic wave. Consequently, efficient wave transmission through the mesh filters is achieved over a frequency range at which electromagnetic wavelength is much larger than the mesh filter feature sizes [26, 27]. After actuating the MEMS switches, the two mesh filters are in contact with each other, exhibiting inductive (high-pass filter) behavior in response to an incident electromagnetic wave. Therefore, efficient wave reflection from the structure is achieved over a frequency range at which electromagnetic wavelength is much larger than the mesh filters’ feature sizes [26, 27]. As a result, by switching the MEMS switches between the contact and non-contact modes, the double-layered mesh filter structure alters between a high-pass (inductive) and low-pass (capacitive) filter, respectively, leading to efficient terahertz modulation over a broad range of frequencies determined by the feature sizes of the mesh filters [26, 27].
In order to implement the broadband terahertz modulator designs based on the discussed MEMS-reconfigurable meta-surfaces [23–25], we have investigated various MEMS switches and mesh filter geometries. On one hand, in order to achieve broad modulation bandwidth, the MEMS switches should be capable of connecting/disconnecting metallic structures with deep subwavelength feature sizes and spacings at terahertz frequencies. On the other hand, the overall size of the reconfigurable mesh filter should be larger than the wavelength of the incident wave not to attenuate terahertz wave transmission by diffraction. Additionally, in order to achieve high modulation speeds and low modulation voltages, the switching time and actuation voltage of the MEMS switches should be lowered while maintaining reliable device operation.
2. Device structure
The schematic diagram of the designed reconfigurable metallic mesh filter and utilized MEMS switches are shown in Figs. 2(a) and 2(b), respectively. The top mesh filter consists of metallic anchors and moving membranes of an array of vertically oriented (along the y-axis) multi-contact MEMS switches with a fixed-fixed beam configuration [Fig. 2(b)]. The bottom mesh filter consists of an array of vertical metallic slits on a silicon substrate with arrays of horizontally oriented (along the x-axis) metallic patches extended outward to serve as the contact pads of the multi-contact MEMS switches. By actuating the MEMS switches between the contact and non-contact modes, the reconfigurable mesh filter structure alters between a high-pass (inductive) and low-pass (capacitive) filter, respectively, modulating the intensity of a horizontally-polarized incident terahertz wave over a broad range of frequencies determined by the feature sizes of the mesh filters . The actuation voltage is applied between the silicon substrate, which serves as the actuation pad of the MEMS switches, and the moving membranes. The moving membranes and metallic patches are electrically connected and isolated from the silicon substrate through use of SiO2 isolation layers under metallic patches.
The horizontal dimension of the MEMS switches and metallic patches and the vertical distance between the metallic patches and contact dimples are selected at the smallest possible limits that can be fabricated with high yield. This is because the switches and metallic patches are implemented in a two-dimensional array and the terahertz modulation bandwidth is inversely proportional to the periodicity of the array in the horizontal and vertical directions [23, 28]. The multi-contact structure is selected for the MEMS switches to minimize the distance between the horizontally oriented metallic patches that serve as the contact pads of the MEMS switches. Using this switch structure, it becomes possible to connect multiple metallic patches at once with horizontal and vertical spacings much smaller than what could be achieved if we were to use individual MEMS switches per each pair of metallic patches. The fixed-fixed beam structure is chosen because of its high spring constant, which is necessary for obtaining high switching speeds. Moreover, the fixed-fixed beam structure is less susceptible to residual stress and stress gradients coming from the fabrication process . The center part of the beam, under which all the contact pads are placed, is designed to be much thicker than the rest of the beam. This part of the beam is intended to behave like a proof mass and to maintain the connection between two metallic patches at the same time, by the help of dimple pairs that are placed underneath the proof mass. The reason for using a thicker center part as a proof mass is to minimize bending of the beam, which will be discussed further in the following section.
3. Switch design
3.1 Mechanical model
The one-dimensional mechanical model shown in Fig. 3 is used as a starting point for designing the fixed-fixed beam MEMS switch. As illustrated in Fig. 3, the presented MEMS switch is modeled as two springs, with spring constant kcg, on both sides of a proof mass that is pulled down by an applied electrical force Fe. The proof mass corresponds to the thicker center part of the beam and the springs correspond to thin support arms on the sides of the beam. Here, we assume that the thin support arms are modeled as cantilevers with guided ends and the thicker center part of the beam hardly bends. These assumptions and the utilized model work fairly well with a high accuracy, which will be discussed further in this section.
As mentioned in the previous section, the switch design targets minimal dimension in the horizontal direction and minimal spacing between contact dimples in the vertical direction, while maintaining an affordable actuation voltage, a high switching speed, and a uniform distribution of contact force when the switch is pulled down. It should be noted that in contrary to RF MEMS switches, having a high contact force is not a design goal for the intended application. This is because a low DC contact resistance is not required for reconfiguring the metallic mesh filter from a capacitive state to an inductive state at terahertz frequencies . In fact, an air gap of 20 nm at the contact point can still provide the intended high modulation depth performance at terahertz frequencies [23, 28]. This design flexibility allows switching operation at relatively low voltages and enables reliable device operation by eliminating the need for applying high electrostatic forces and direct metal-to-metal contact [30, 31].
As the first design parameter, the width of the MEMS switch, w, is selected as 10 µm, which is the smallest dimension that can be fabricated safely considering the fabrication constraints of the dimple pairs placed underneath the beam. The selected width also reduces the susceptibility of lateral bending of the thin support arms on both sides due to residual stress. The length of the thin support arms, l1, is chosen so that the thin support arms have a moderate spring constant in order to have an affordable actuation voltage and a reasonably high restoring force, which is the critical parameter for the switching speed of the switch. The actuation voltage can be estimated as :33]:Fig. 4(a). Following this analysis, the length of the thin support arms, l1, is selected as 10 µm to achieve a moderate actuation voltage while maintaining the miniaturization requirement for broadband terahertz modulation.
Apart from the actuation voltage value, the maximum bending of the beam is another important factor that should be taken into account when selecting the device geometry. In this regard, the length of the thicker center part of the beam, l2, should be short enough to prevent bending of the beam during actuation and its thickness, t2, should be large enough to keep the beam as flat as possible. Figure 4(b) shows the amount of beam deflection as a function of the length and thickness of the thicker center part of the beam for a simply supported beam model. It should be mentioned that the simply supported beam is not the most accurate model for the thicker center part of the beam. However, it is known that the deflection of the thicker center part of the beam is less than that of a simply supported beam. Therefore, we use the deflection value estimated by the simply supported beam model to calculate the worst case scenario for the bending of the beam in the presented design.
Following this analysis and using the graphs presented in Fig. 4, the length and thickness of the thicker center part of the beam, are selected as 40 µm and 1.25 µm, respectively, which result in an actuation voltage of 39.5 V and a beam deflection of less than 0.03 µm. It should be also noted that the effects of the dimples are not taken into account for the initial design of the MEMS switch and will be further investigated in the following sections. Following the initial design of the MEMS switch based on the simply supported beam model, performance of the designed MEMS switch is analyzed using a three-dimensional finite element solver, Coventorware . The simulation results show that the designed beam has a spring constant of 27 N/m and an actuation voltage of 40 V, which are in close agreement with the analytical predictions of 24.4 N/m and 39.5 V, respectively. Also, the maximum deflection of the thicker center part of the beam calculated by Coventorware is 0.026 µm under an applied voltage is 39 V, which is less than the maximum deflection value of 0.03 µm predicted by the discussed beam model [Fig. 4(b)]. It should be noted that the applied force for the maximum deflection analysis is the electrical force under an applied voltage of 39 V, which is the maximum voltage value before the beam is pulled in.
After selecting the dimensions of the beam, the next step is to determine the number and arrangement of the dimple pairs that are used for connecting the metallic patch pairs on either side of the beam. On one hand, the dimple pairs are required to be placed at a minimal distance in the vertical direction in order to achieve broadband modulation performance [23, 28]. On the other hand, a contact gap of less than 20 nm is required for each dimple pair when the switch is pulled down. This is because an air gap of 20 nm at the contact point can still provide the intended high modulation depth performance at terahertz frequencies [23, 28]. A set of Coventorware simulations are performed for the designed beam and the performance of the MEMS switch is analyzed for different number of dimple pairs, n, placed under the beam. Table 1 presents the actuation voltage of the MEMS switch for different number of dimple pairs. As the results indicate, the actuation voltage increases slightly as the number of dimples is increased due to the decrease in the actuation pad area. This also implies that the applied electrical force decreases as the number of dimple pairs is increased. The failure voltage of the MEMS switch is also investigated for different number of dimple pairs and calculated to be greater than 200 V for all cases except for the case of two dimple pairs, where the failure voltage is 130 V.
Coventorware simulation results also indicate that although the dimple pairs close to the center of the beam contact their corresponding metallic patches at an applied voltage of 40 V, the side dimple pairs do not contact their corresponding metallic patches unless the voltage is increased significantly. This is not preferred for most practical applications. However, as mentioned before, a complete contact is not required for device operation at terahertz frequencies and a contact gap of less than 20 nm can still provide the intended high modulation depth performance at terahertz frequencies [23, 28]. Therefore, in order to maintain relatively low actuation voltage levels, the number of dimple pairs is selected as four. Use of four dimple pairs results in a sufficiently short distance between dimple pairs (sd = 12 µm), which is required for a terahertz modulation bandwidth of more than 3 THz. Additionally, an applied voltage of 92 V is sufficient for obtaining a contact gap of less than 20 nm for all four dimple pairs. The Coventorware simulation results for the designed MEMS switch with four dimple pairs at 40 V and 92 V are shown in Figs. 5(a) and 5(b), respectively. The results indicate that the contact gap between the side dimples and their corresponding metallic patches reduce from 90 nm to 18.6 nm when increasing the applied voltage from 40 V to 92 V, which is much smaller than the failure voltage of the MEMS switch.
The next step of the design is selection of anchor point length, la, which adds to the total length of the beam and needs to be minimized to maintain a small array periodicity in the vertical direction. The key is to ensure that the anchor point operates as a fixed point for the beam and to prevent bending at this point due to reaction force. To investigate the impact of the anchor length, the MEMS switch is analyzed using Coventorware for anchor lengths ranging from 2 µm to 10 µm. The results show no significant bending at the anchor point even for an anchor length of 2 µm. Following this analysis, the anchor length is selected as 5 µm contemplating possible fabrication limitations. The dimensions of the final design are shown in Table 2.
3.2 Dynamic analysis
Dynamic analysis of the presented MEMS switch is important since the switching speed of the MEMS switch determines the terahertz modulation speed. The time domain mechanical response of the MEMS switch is determined by the following differential equation :32] and the quality factor of the beam is calculated as 23.6 using Q = k / (2πf0b).
For calculating the actuation time, the electrical force is considered to be constant and the damping factor is considered to be negligible, which accurately model systems with small damping factors and quality factors larger than 2 [32, 36]. For calculating the release time, when no electrical force is present, the damping factor is taken into account. The actuation and release times are calculated using the solutions of (3) as 1.49 µs and 0.89 µs, respectively, which are in close agreement with the Coventorware simulation results of 1.48 µs and 1.05 µs, respectively. The total response time in actuation and release can be as high as two times of these values due to the bumping or settling of the MEMS switch , predicting a terahertz modulation speed of 200 kHz. It should be noted that the total stray capacitance and distributed interconnection resistance of the array of MEMS switches are estimated to be 76 pF and 800 Ω, respectively, estimating an electrostatic actuation cutoff frequency of about 2.6 MHz. Therefore, the modulation speed of the designed terahertz modulator is limited by the mechanical resonance frequency of the MEMS switches. It should be also noted that the presented MEMS switch is designed for use in a proof of concept terahertz modulator and its switching speed can be easily increased by an order of magnitude by increasing the mechanical resonance frequency of the beam [29, 37], which makes it possible to obtain terahertz modulation speeds of several MHz.
3.3 Stress analysis
The thin support arms of the MEMS switch are realized using a 0.25 μm thick sputtered gold layer, whereas the thicker center part of the switch is implemented using a 1.25 μm thick electroplated gold layer to obtain the desired thickness of 1.25 μm. Residual stress and stress gradients in the metallic thin films have important impact on performance of the MEMS switches and cause undesired buckling of the beams . While sputtered gold thin films often result in residual stress , electroplated gold thin films usually exhibit stress gradient within the film due to their higher thicknesses . The impacts of the residual stress in the sputtered gold layer and stress gradient in the electroplated gold layer are analyzed using Coventorware. It should be noted that the residual stress in the sputtered gold layer and stress gradient in the electroplated gold layer can result in a positive (upward) or negative (downward) deflection in the beam. Although a positive beam deflection impacts the MEMS switch performance by increasing its actuation voltage, it does not result in device failure. However, a negative beam deflection could lead to the failure of the MEMS switch. Figure 6(a) shows the simulated beam deflection as a function of the residual stress in the sputtered gold layer, while assuming no residual stress and stress gradient in the electroplated gold layer. The simulation results indicate a downward buckling for tensile residual stress values up to +150 MPa and an upward buckling for compressive residual stress values down to −100 MPa, which is expected due to the thicker center part of the fixed-fixed beam. However, after the residual stress is increased further onto the compressive side, exceeding the critical stress , the beam shows a downward buckling due to the shape of discontinuities of the beam. Using Coventorware, the critical stress is estimated to be −144 MPa and the beam deflection is estimated to be more than 300 nm for a compressive stress of −150 MPa. Figure 6(b) shows the estimated beam deflection as a function of the stress gradient in the electroplated gold layer, while assuming no residual stress in the sputtered gold layer. The results indicate less than 0.1 μm beam deflection for residual stress gradients up to +100 MPa/μm, which is a wide stress gradient range considering the values reported in literature .
Since the residual stress and stress gradient can impact the specifications of the designed MEMS switch, the actuation voltage of the designed MEMS switch is investigated under stress conditions using Coventorware. While the stress gradient of the electroplated gold layer shows a minor effect on the actuation voltage, the residual stress of the sputtered gold layer shows a more substantial effect on the actuation voltage. The simulation results indicate less than 15% change in the actuation voltage for residual stress values ranging from 150 MPa to −50 MPa. However, the actuation voltage starts to increase significantly for residual stress values ranging from −50 MPa to −100 MPa, reaching 58.5 V at −100 MPa. On the other hand, the actuation voltage is reduced for residual stress values ranging from −100 MPa to −150 MPa, reaching 26.5 V for a residual stress value of −150 MPa. This is due to the reduction in the gap between the beam and actuation pad for residual stress values ranging from −100 MPa to −150 MPa. The spring constant for this case is calculated as 24.7 N/m, showing a slight reduction compared to the spring constant of 27 N/m in the absence of the residual stress. Investigating different stress scenarios shows that none of the above mentioned residual stress and stress gradient values can cause a device failure since the gap between the upper and lower mesh filters will be always greater than 250 nm in the MEMS switch non-contact state .
The reconfigurable metallic mesh filter based on the designed MEMS switch is fabricated on a silicon substrate using a five-layer, six-mask surface micromachining process. The device has an active area of 1 mm × 1 mm, consisting of 938 MEMS switches, surrounded by a metal frame. The metal frame is used as an aperture to focus an incident terahertz beam onto the device active area. All the MEMS switches are electrically connected to be able to switch the entire array with a single control voltage. The summary of the fabrication process is shown in Fig. 7. The silicon substrate is a p-type substrate with a resistivity of 40 Ohm-cm, which is selected in order to minimize terahertz wave propagation losses in the substrate.
The fabrication process starts with the definition of the actuation pad areas (mask 1) on the silicon substrate using reactive ion etching (RIE) [Fig. 7(a)]. Then, the SiO2 layer is deposited using plasma enhanced chemical vapor deposition (PECVD) in order to fill the remaining areas, which is followed by the planarization step, performed using chemical mechanical polishing (CMP) [Fig. 7(b)]. The first metal layer (Ti/Au - 100/1000 Å) is deposited using sputtering and patterned to define the bottom mesh filter (mask 2) [Fig. 7(c)]. The sacrificial layer (PMMA/PMGI - 6000/2500 Å) is spin-coated and patterned to open the anchor points of the MEMS switches (mask 3) [Fig. 7(d)]. Then, the dimples of the MEMS switches are defined (mask 4) [Fig. 7(e)]. The second metal layer (Ti/Au - 100/2500 Å) is deposited using sputtering for the thin support arms of the MEMS switches. This layer also serves as a seed layer for the following electroplating step [Fig. 7(f)]. The third metal layer (Au - 1.25 μm) is electroplated to form the thicker center parts of the MEMS switches and the anchor areas (mask 5) [Fig. 7(g)]. Finally, the remaining parts of the second metal layer are removed (mask 6), the sacrificial layer is etched, and the structures are released using critical point drying (CPD) [Fig. 7(h)].
Top view microscope image of the fabricated MEMS-reconfigurable mesh filter, top view scanning electron microscope (SEM) image of the fabricated MEMS switches, and side view SEM image of the moving membrane of one of the MEMS switches are shown in Figs. 8(a)-8(c).
5. Measurement results
5.1 Stress measurements
The residual stress and stress gradient of the sputtered and electroplated gold layers are measured using specifically designed micromachined test structures [40–42]. The measurement results show an excessive compressive residual stress of around −150 MPa in the sputtered gold layer, which is due to the Ti adhesion layer, resulting in a downward deflection of 300 nm in the beam. This result is also consistent with Coventorware simulations. As explained before, 300 nm downward deflection does not cause any failure of the MEMS switch, and hence, the reconfigurable mesh filter. Figures 9(a) and 9(b) show surface profile of the fabricated MEMS switch and three-dimensional surface profile of an array of the MEMS switches in the fabricated reconfigurable mesh filter, measured with an optical profilometry system. The measured surface profiles indicate almost identical surface profiles for different MEMS switches across the entire device area.
5.2 Mechanical characterization
Mechanical specifications of the fabricated devices are characterized statically and dynamically. For the static characterization, the actuation voltages of single MEMS switches are measured and their spring constants are extracted from this measurement. This is done by measuring the contact resistance of single MEMS switches as a function of the applied voltage. While an open-circuit contact is observed at low voltage values, an abrupt drop in contact resistance is observed at 30 V, which indicates an actuation voltage of 30 V. At higher voltage levels, the contact resistance drops gradually as a function of voltage, indicating an increase in contact force. The measured actuation voltage of 30 V for single MEMS switches is in agreement with the measured terahertz modulation voltage of the fabricated reconfigurable mesh filter (as described in the next section). The measured actuation voltage of 30 V is also close to the 26.5 V actuation voltage value estimated by Coventorware under −150 MPa compressive stress. The extracted spring constant is calculated as 28.1 N/m, which is also close to the 24.2 N/m spring constant value estimated by Coventorware under the same stress conditions.
For the dynamic characterization, frequency response of the MEMS switches is measured using a Polytec MSA 500 dynamic MEMS analyzer system at a 0 V DC voltage and a 5 V AC voltage set to be smaller than the MEMS switch actuation voltage [Fig. 10]. The measurement results show that the MEMS switches have a mechanical resonance (fundamental mode) of f0 = 272 kHz, which is in close agreement with the design values of f0 = 262 kHz. The measurement results also indicate a quality factor of Q = 5.2 for the MEMS switches, which is close to the estimated quality factor of Q = 6.4 under 150 MPa compressive stress with a beam deflection of 300 nm and a damping factor of 2.6 µN·s/m .
The actuation time, tr, is extracted as 1.23 μs, which is also fairly close to the estimated value 1.48 μs. These measurements show that the spring constant, effective mass, and material parameters are accurately modeled. Table 3 summarizes the comparison between the measured and estimated design parameters.
5.3 Modulation characterization
Modulation performance of the fabricated MEMS-reconfigurable mesh filter is characterized using a time-domain terahertz spectroscopy setup . A terahertz pulse is focused onto the device active area and power spectrum of transmitted terahertz beam through the device is analyzed at various voltages within 0.1-1.5 THz frequency range. The device is mounted on a rotation mount to align the polarization of the incident terahertz beam in the horizontal direction (along the x-axis). The details of the modulation characterization process are given in .
The experimental results indicate ~50% power transmissivity at 0 V (modulation OFF state). The observed 50% power attenuation is dominated by Fresnel reflections at air-silicon interfaces and can be eliminated by thinning down the silicon substrate under the device active area . The power of the transmitted terahertz beam decreases as we increase the applied voltage, due to reduction in the gap between the contact dimples and their corresponding contact pads. The power of the transmitted terahertz beam reaches its lowest value at 30 V and stops decreasing beyond 30 V (modulation ON state). This indicates that all the contact dimples have reached within ~20 nm distance from their corresponding contact pads at 30 V, which is close to the estimated actuation voltage of 26.5 V. Figure 11(a) shows the spectrum of the transmitted terahertz power through the device at 0 V and 30 V. It indicates a record high modulation depth of more than 70% over a broad terahertz frequency range of 0.1-1.5 THz. The observed spectral dips in the spectrum are the result of the metal frames used for focusing the incident terahertz beam onto the device active area. Figure 11(b) shows the modulation depth of the terahertz pulse as a function of modulation speed, indicating modulation speeds exceeding 20 kHz. It should be mentioned that although modulation speeds as high as 200 kHz are expected for the device, the measured modulation speed is bound by frequency limitations of the utilized experimental setup. Finally, the lifetime of the fabricated MEMS-reconfigurable filter is investigated under various modulation speeds in the 1-20 kHz range, indicating no failure or degradation in the device modulation depth after accumulating more than 50 billion modulation cycles.
In summary, a miniature multi-contact MEMS switch is specifically designed and optimized for use in a reconfigurable metallic mesh filter for broadband terahertz modulation. The design targets minimal mesh filter dimensions, to achieve a broad modulation bandwidth, while maintaining a relatively low actuation voltage and a high switching speed, which determine the modulation voltage and modulation speed, respectively. The MEMS switch is designed using a simply supported beam model and its specifications are characterized using Coventorware under various stress conditions. The optimized design is fabricated on a silicon substrate and its mechanical, electrical, and electromagnetic properties are characterized subsequently. The experimental results show that the use of the designed miniature MEMS switch in a reconfigurable filter offers a record high modulation depth of more than 70% over a broad terahertz frequency range of 0.1-1.5 THz with a modulation voltage of 30 V and modulation speeds exceeding 20 kHz.
The authors would like to thank Dr. Christopher W. Berry for his help with device characterization at terahertz frequencies; Shang-Hua Yang for his help with device fabrication; Prof. Kivanc Azgin, Orhan Sevket Akar and METU MEMS Center personnel for their help with the laser vibrometer measurements; Lurie Nanofabrication Facility (LNF) personnel, especially Dr. Robert Hower, for their support during device fabrication; and Prof. Husnu Dal for valuable discussions on the beam theory. The authors gratefully acknowledge the financial support from National Science Foundation Sensor and Sensing Systems division (Contract # 1030270) and Army Research Office Young Investigator Award (Contract # W911NF-12-1-0253).
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