RF MEMS Varactor
MEMS varactors have considerable advantages compared with other semiconductor devices, including low loss, very high Q at mm-wave frequencies, high power handling capability, low power consumption, and high IIP3. An RF MEMS switch or varactor usually includes two parts: the electrical part and the actuation part. Here, the mechanical movements can be obtained from electrostatic, magnetostatic, piezoelectric, or thermal force . The electrostatic actuation method is the most widely used technique since it has virtually zero power consumption, small electrode size, thin layers used, relatively short switching time, 50-200 µN of achievable contact forces and provides the possibility of biasing the switch or varactor using high resistance bias lines .
Currently, there are three different standard technologies for MEMS varactor designs. The first one employs a parallel-plate structure. The variable capacitance can be achieved by providing DC bias to vertically change the gap between the parallel plates. The second one features an inter-digital structure. The variable capacitance can also be achieved by providing the DC bias, but in this case to horizontally change the gap between the comb fingers. The third utilizes MEMS switches to select the required capacitance from fixed-valued capacitance banks .
The “conventional” RF-MEMS varactor is essentially a parallel plate capacitor whose capacitance is determined by the spacing between a fixed bottom plate and a movable suspended top plate. Electrostatic actuation occurs when an electrostatic force is created by applying a DC voltage between the capacitor plates, thereby displacing the movable plate toward the fixed plate. The schematic and the actuation functions of the shunt capacitive type RF MEMS switch are shown in Fig. 1 and Fig. 2, respectively.
In the “up” state, there is an air gap between the top movable metal beam and the bottom metal beam. This air gap forms a high impedance to DC. When a DC voltage is applied between the two metal beams, the top beam will be pulled down due to the electrostatic force. If the applied voltage exceeds the pull-down voltage (VP), the top metal beam will be pulled down directly on the dielectric surface, which is defined as the “down” state. The capacitance increases dramatically, and the RF path is shorted to ground. When varying the applied DC voltage between zero to the actuation voltage, the air gap between the two metal beams will also change. This will form the “middle” state and the capacitance of the switch will change with the DC bias. Thus, the MEMS switch acts as a varactor.
The RF MEMS varactor can be employed in the phase shifter or true time delay line design to replace the GaAs Schottky varactor diode for low-loss, broadband, and high frequency applications in modern communication, automotive and defense applications.
Fig. 1 Schematic of shunt capacitive type RF MEMS switch
Fig.2 Functions of shunt capacitive type RF MEMS switch
The standard capacitive MEMS switch/varactor model comprises a parallel-plate capacitor which includes a fixed bottom metal plate and a moveable top metal plate and a linear spring with spring constant k.
We know that the electrostatic potential energy is:
The electrostatic force is therefore:
The mechanical spring force is:
Equilibrium occurs when the mechanical spring force on the suspended plate equals the electrostatic force of the parallel-plate capacitor. From these, we can derive:
When, we can find that:
Consequently, the equilibrium exists only when 0 ≤ x ≤ xo/3. Beyond this limit, the electrostatic force overcomes the spring force causing the two plates to quickly snap into contact. This is known as the pull-in effect , and limits the theoretical maximum capacitance ratio Cmax/Cmin of the conventional MEMS capacitive varactor to 1.5.
The pull-in effect is the major limitation in MEMS varactor designs. It will cause nonlinearity and mechanical instability of the MEMS varactors. In order to avoid the snap down, the designed capacitance ratio of the conventional MEMS capacitive varactor is usually set to 1.2 to 1.5.
In order to eliminate the pull-in effect and increase the capacitance ratio of MEMS varactors, researchers have invented a variety of clever concepts.
Take MEMS Extended Tuning Range Varactor Structure for example.
One of the extended tuning range RF MEMS varactor structures is designed with separate actuation parts and signal electrodes. A schematic diagram of such a structure is plotted in Fig. 3.
According to the above model structure and the equations derived from the conventional MEMS varactor, the maximum capacitance tuning range of the extended tuning range structure is:
If the distance d1 between the two signal electrodes E1 and E2 is, the upper beam E1 is constrained to travel a maximum distance of d1 before the pull-in effect happens between the actuation pads. Thus, the theoretical capacitance tuning range can theoretically approach infinity .
EM Modeling in Ansoft HFSS®
A Phased Antenna Array, working from 50 GHz to 70 GHz for the DIII-D tokamak project  in San Diego is needed. The simulation results are shown as follows.
Fig.4 Ansoft HFSS® 3-D EM single MEMS varactor model
The single MEMS varactor model is shown in Fig.4. The MEMS varactor is symmetric along the center of the CPW transmission line. Therefore, in order to save simulation time, we can use a Symmetric H plane to cut the MEMS varactor along the center line into two equal pieces, as shown in Fig.5.
Fig.5 Simplified Ansoft HFSS® 3-D EM single MEMS varactor model
We need to cascade several varactor elements to realize 360°delayed phase, since it is hard to achieve for one single element.
In this design, eighteen elements are used, which is shown in Fig.6.
Fig.6 18-element MEMS delay line EM model based on MEMS varactor design
S-parameter simulation results of the MEMS extended tuning range varactor based true time delay line design are shown in Fig.7 to Fig.9.
Fig.7 Magnitude of S11 in decibels at different states
Fig.8 Magnitude of S21 in decibels at different states
Fig.9 Delayed Phase of S21 in degrees between different states
From Fig.7 to Fig.9, we can see that from 50 GHz to 70 GHz, the predicted values are (d=0.825 µm, navy line in Fig.7 and Fig.8, olive line in Fig.9): Minimum Return Loss is below -10 dB, Maximum Insertion Loss=-3.26 dB, Min(angle difference) exceeds 360 degrees.
In the RF MEMS extended tuning range varactor design, a 380 µm thick high-resistivity Si substrate with dielectric constant of 11.9 and resistivity >7000 Ω-cm has been chosen since this substrate material has low substrate loss and the fabrication process is compatible with conventional IC processes.
The most important and difficult part of this design is to form the variable height top metal beam. In order to realize this structure, a five-mask fabrication process has been designed by using surface micromachining technology and the fabrication process flow chart is shown in Fig. 10.
Fig.10 Fabrication Procedure
(a) Use Thermal Oxidation to grow a 0.2 µm SiO2 buffer layer on a 380 µm high-resistivity Si wafer (7000-10,000 ohm-cm)
(b) Use lift-off to form 0.7 µm gold CPW lines and bias pads, and 0.7 µm SiCr actuation pads
(c) Use PECVD to grow a 0.3 µm Si3N4 and use RIE to form the dielectric layer
(d) Spin 1 µm PR to form the first sacrificial layer and pattern the anchors
(e) Spin 2 µm PR to form the second sacrificial layer and pattern the anchors and the CPW center conductor
(f) Remove center of the PR2 by patterning
(g) Electroplating 2 µm gold to form the upper beam
(h) Remove the sacrificial layer and release the whole structure
 Gabriel M. Rebeiz, “RF MEMS Theory, Design, and Technology,” John Wiley & Sons, Inc., Hoboken, New Jersey, 2003.
 S.D. Senturia, “Microsystem Design,” Kluwer Academic Publishers, Boston, MA 2001.
 Yaping Liang, C.W. Domier, and N.C. Luhmann, Jr., “MEMS Based True Time Delay Technology for Phased Antenna Array Systems”, Proceedings of Asia-Pacific Microwave Conference 2007