EE 571 INTRODUCTION TO MEMS
A REVIEW ON RF MEMS SWITCHES
SUBMITTED BY: GÖKSENİN BOZDAĞ
SUBMITTED TO: Asst. Prof. MÜJDAT BALANTEKİN
December 2012
CONTENTS
A. ............................................................ .................................................................................................................................. ................................................................................................. ........................... 3
1.
WHAT IS MEMS ? .......................................................................................................... .......................................................................................................................... ................ 3
2.
WHAT IS RF MEMS ? ................................................................................................................ ..................................................................................................................... ..... 3
3.
RF MEMS SWITCHES .................................................................... ..................................................................................................................... ................................................. 4
4. ADVANTAGES AND DISADVANTAGES OF RF MEMS SWITCHES ...................................................... ...................................................... 7
B............................................................................................................................................................. B............................................................................................................................................................. 1 0
1.
DESIGN OF A LATERAL RF MEMS SERIES SWITCH SWIT CH ................................................................... 10 1.1
ELECTRICAL DESIGN AND SIMULATION ............................................................... ............................................................................. .............. 10
1.2
MECHANICAL DESIGN AND SIMULATION ............................................................ .......................................................................... .............. 23 1.2.1 STATIC ELECTROSTATIC FORCE ............................................................... ............................................................................. .............. 24 1.2.2 STATIC RESTORING RES TORING FORCE ........................................................... .................................................................................... ......................... 25 1.2.3 STATIC THRESHOLD VOLTAGE .............................................................................. .............................................................................. 27 1.2.4 DYNAMIC FREQUENCY RESPONSE ......................................................... ....................................................................... .............. 28 1.2.5 DYNAMIC EFFECTIVE MASS ...................................................................... ................................................................................. ........... 29
2.
CONCLUSION AND FUTURE WORK WOR K ....................................................................................... .......................................................................................... ... 36 36
C. ............................................................................................................................... ........................................................................................................................................................ ......................... 37
REFERENCES.................................................................................................................................. 37
CONTENTS
A. ............................................................ .................................................................................................................................. ................................................................................................. ........................... 3
1.
WHAT IS MEMS ? .......................................................................................................... .......................................................................................................................... ................ 3
2.
WHAT IS RF MEMS ? ................................................................................................................ ..................................................................................................................... ..... 3
3.
RF MEMS SWITCHES .................................................................... ..................................................................................................................... ................................................. 4
4. ADVANTAGES AND DISADVANTAGES OF RF MEMS SWITCHES ...................................................... ...................................................... 7
B............................................................................................................................................................. B............................................................................................................................................................. 1 0
1.
DESIGN OF A LATERAL RF MEMS SERIES SWITCH SWIT CH ................................................................... 10 1.1
ELECTRICAL DESIGN AND SIMULATION ............................................................... ............................................................................. .............. 10
1.2
MECHANICAL DESIGN AND SIMULATION ............................................................ .......................................................................... .............. 23 1.2.1 STATIC ELECTROSTATIC FORCE ............................................................... ............................................................................. .............. 24 1.2.2 STATIC RESTORING RES TORING FORCE ........................................................... .................................................................................... ......................... 25 1.2.3 STATIC THRESHOLD VOLTAGE .............................................................................. .............................................................................. 27 1.2.4 DYNAMIC FREQUENCY RESPONSE ......................................................... ....................................................................... .............. 28 1.2.5 DYNAMIC EFFECTIVE MASS ...................................................................... ................................................................................. ........... 29
2.
CONCLUSION AND FUTURE WORK WOR K ....................................................................................... .......................................................................................... ... 36 36
C. ............................................................................................................................... ........................................................................................................................................................ ......................... 37
REFERENCES.................................................................................................................................. 37
A. 1.
WHAT IS MEMS ?
Micro-Electro-Mechanical Systems (MEMS) is a technology that in its most general form can be defined as miniaturized mechanical and electromechanical elements (i.e., devices and structures) that are made using the techniques of micro fabrication. The critical physical dimensions of MEMS devices can vary from well below one micron on the lower end of the dimensional spectrum, all the way to several millimetres. MEMS is the integration of a number of micro components on a single chip which allows the microsystem to both sense and control the environment. [1]
2.
WHAT IS RF MEMS ?
RF MEMS acronym refers to electronic components of which moving submillimeter-sized millimeter-sized parts provide RF functionality.[2] Today, RF-MEMS has been an attractive field for both scientific research and industry due to its promising application in future civil & military wireless communication and remote controlling & sensing system. There are various types of quintessential RF MEMS components, such as RF MEMS resonators and oscillators, RF MEMS tuneable inductors and RF MEMS switches, switched capacitors and varactors.[1]
Figure 1 a)SEM of MEMS Switch
b) A two-pole 7 MHz Filter
3.
RF MEMS SWITCHES
RF MEMS switches are micro machined devices which use a mechanical movement to achieve a short circuit or an open circuit in the RF transmission line. RF MEMS switches can be classified by actuation method (electrostatic, electro thermal, magnetic, piezoelectric), axis of deflection (lateral, vertical), circuit configuration (series, shunt), clamp configuration (cantilever, fixed-fixed beam) or contact interface (capacitive, ohmic). [3]
Table 1 Different Configurations of MEMS Switches [4]
There are two main types of forces that can be used for the actuation of RF Switches: Electromagnetic and Electrostatic . The electromagnetic force has a low actuation voltage, but a high current consumption. On the other hand, the electrostatic force has no current consumption, but has a high actuation voltage. The electrostatic switches are most common switches that are used in the microwave and mm-wave regions. Electro statically actuated RF MEMS components offer low insertion loss and high isolation, linearity, power handling and Q factor. There are two kinds of electrostatic switches: Series and Shunt. Both ohmic and capacitive coupling switches can be used either as a serial or a shunt switch, generally ohmic switches are used in serial mode while capacitive coupling switches are preferred as shunt switches. Series switch is initially disconnected and gets connected when the switch is actuated. Shunt switch is initially connected, and gets disconnected when a required voltage is applied. For a capacitive shunt switch showed in Figure 2(a), the transmission line is normally ON and there is a dielectric layer laid between switch membrane and transmission line. When membrane is pulled down, it will form a parallel plate capacitor structure. The RF signal will be conducted to ground via the capacitor. The RF characteristics of this type are affected by capacitance ratio between ON/OFF state and because of its principal the isolation characteristic of this type will be better at higher frequency. If apply a DC voltage so that both ends of the switch are charged differently and create an electrostatic force. This force causes an attraction between the two areas. The attractive force causes the switch to close. This allows the RF power to flow through the switch but the dielectric layer does not allow the electricity to flow through. When the voltage is turned off the switch open back due to the dielectric layer. Without the dielectric layer the DC current would flow through the switch causing it to stick closed permanently. It would be a onetime switch. For a series-contact switch showed in Figure 2(b) the signal transmission line is normally OFF, it means the signal will pass the line only when the switch membrane is pulled down and the conductor touches both side of gap on transmission line. This type has good isolation characteristic from DC to RF signal, but the insertion loss control and reliability are the issues need to be noted. It is because self-welding may happen at the metal-to –metal contact
area between membrane and transmission line. The series contact switch, the beam in the up position corresponds to a low-loss RF path to the output load, while the beam in the down position results in RF shunted to ground and no RF signal at the output load capacitive reactance restricts high quality performance to high RF signal frequencies (5-100 GHz), whereas the contact switch can be used from dc levels.
Figure 2 a) A Capacitive Fixed-fixed Beam RF MEMS Switch, Connected in Shunt to a CPW Line. b) An Ohmic Cantilever RF MEMS Switch, Connected in Series to a Micro Strip.
Series and shunt switches can be roughly compared as Table 2. Type
Advantage
Disadvantage
Series
Very low ON insertion loss Very high OFF isolation
Shunt
Long Life Time High Potentials Independent from contact force Table 2
Stiction Microscopic banding
4. ADVANTAGES AND DISADVANTAGES OF RF MEMS SWITCHES
Table 3 shows a comparison between electrostatic MEMS switches and GaAs PIN diode and transistor switches. It is hard to make an accurate comparison over a wide range of RF power levels since the size of diode and transistor switches can be easily increased for high power applications.[4]
Table 3
On the other hand, we can summarize the advantages of RF MEMS switches over PIN diode and FET switches: Near Zero Power Consumption : The electrostatic actuation requires almost 3080 V, but does not pass any current. So the power consumption is almost zero, which is an excellent characteristic of RF MEMS switch. On the other hand, thermal or magnetic switches consume a lot of current. Very low insertion loss: RF MEMS metal contact and capacitive switches have an insertion loss of 0.1 db even at 100 GHz.
Very high isolation: RF MEMS switches are fabricated with air gaps and therefore have a very low capacitance resulting in excellent isolation at even high frequencies of the order of 100 GHz.
Figure 3 Simulated isolation of MEMS, PIN, and FET series switches. Potential for low cost : RF MEMS are fabricated on quartz or silicon, which are not costly materials, but the packaging cost is high due to which the net cost of RF switches increases. Linearity and Inter-modulation products : MEMS switches are extremely linear devices, and therefore result in low inter-modulation products in switching and tuning operations. Their performance is far better than PIN diode or FETs.
RF MEMS Switches also have some problems or disadvantages and these are: Relatively Low Speeds: The switching speed of most electrostatic MEMS switches is 2-40μs, and thermal/magnetic switches are 200-3,000μs. High Voltage or High Current Drive: Electrostatic MEMS switches require 3080V. Thermal/magnetic switches can be actuated using 2-5 V, but require 10100 mA of actuation current.
Power Handling: Most MEMS switches can not handle more than 200mW although some switches have shown up to 500 mW power handling. Reliability: The reliability of mature MEMS switches is 0.1-40 Billion cycles. However, many systems require switches with 20-200 Billioncycles. If we talking about reliability issues in detail, we have extra five cases for both ohmic and capacitive switches. Contamination: contact resistance increases due to organic deposits, absorbed hydrocarbon layers and contamination around the contact area. Can be avoided by proper material selection. Stiction: Arises when the surface interaction energy at a contact point is greater than the restoring force which tends to bring the switch into the equilibrium/open position. In such a case the RF MEMS switch will stick in the closed position. At high current conditions, stiction will generally be generated by hot-welding. Can be avoided by using stiff elements. Wear: The contact may be damaged by a large impact force which can be much greater than the high static contact force needed for low contact resistance. Cycling mode: In cold switching contact damage, pitting, and hardening of the metal occur since the same point is repeatedly hit during cycling. In the long term the contact area is reduced, increasing the contact resistance. In hot switching, metal arcs are produced at contact melting the asperities thereby increasing the area. Dielectric charging : This reliability issue is applicable only for capacitive switches. The theory of dielectric charging involves the concept of charges tunneling into the dielectric and becoming trapped. In an effort to maximize the on-capacitance of a MEMS capacitive switch, the dielectric is typically made quite thin, usually less than 3000 A0.
Packaging: MEMS switches need to be packaged in inert atmospheres (Nitrogen, Argon, etc..) and in very low humidity, resulting in hermetic or near hermetic seals.
Cost: While MEMS switches have the potential of very low cost manufacturing, one must add the cost of the packaging and the high-voltage drive chip.
B.
1.
DESIGN OF A LATERAL RF MEMS SERIES SWITCH
The objective of this part is to design a lateral RF MEMS series switch. The main reasons of designing lateral switches are reliable mechanical performance and simple fabrication process. The switch consists of a transmission line and a cantilever beam. The switch connects or disconnects with the RF circuit by the in-plane motion of the cantilever beam and the coplanar waveguide (CPW) transmission line is used to configure the switch. In this design, using CPW has more advantages than using microstrip line,they are, lower loss tangent than mirostrip so signal couple mostly through air, only need one side of board accesible, no plated holes needed, allows variation of trace width, or spacing-to-ground or dielectric thickness to control Zo, Zo of CPW decreases as dielectric thickness increases, *CPW produces smaller trace per given Zo than Microstrip.[7] This part is organized as follows. First, the RF design, circuit modeling and simulation of the lateral RF MEMS switch are presented. The RF performance of the switch can be improved by optimizing the electrical parameters of the switch.Then, the mechanical design and optimization of the cantilever beam of the lateral switch are discussed. [10]
1.1 ELECTRICAL DESIGN AND SIMULATION RF circuit design and the lumped-element modeling of the lateral switch are discussed in this part of the report. The main purpose is to study the effect of the design parameters and to realize lateral switches with low insertion loss, high return loss, and high isolation. A lateral switch consists of a CPW and an electrostatic actuator, as shown in Figure 4. A cantilever beam is fixed at one port. The free end of the cantilever beam comes into contact with the contact bump at the other port upon turning on the switch. The cantilever beam serves as the signal line alone. The ground lines beside the cantilever beam are extended toward the cantilever beam to
avoid drastic increase in the characteristic impedance. At the free end of the cantilever beam, one ground line protrudes toward the cantilever beam further to serve as a fixed electrode. Therefore, no additional fixed electrode is required. When sufficient DC bias voltage is applied between the cantilever beam and the ground line, the cantilever beam is pulled toward the fixed electrode by electrostatic force until its free end hits the contact bump, resulting in the on-state of the switch. When DC bias voltage is removed, the mechanical stress of the beam overcomes the stiction forces and pulls the cantilever beam away, resulting in the off-state of the switch. Due to the asymmetrical layout of the two ports, the S-parameters obtained from the two ports are not reciprocal. The return loss of port 2 is better than that of port 1 at the off-state since the open stub at port 2 is shorter than port 1. Hence, generally port 2 acts as the input port and port 1 acts as the output port to block more RF signal at the off-state of the switch.
Figure 4 Top view of a lateral switch
1.1.1 RF CIRCIT MODEL OF LATERAL SWITCH Figure 5 shows the equivalent circuit of the lateral switch. The model consists of a characteristic impedance (Z0) for the input and output sections of the CPW; a line resistor (Rl) of the cantilever beam; a line inductor (L) of the cantilever beam; a switch series capacitor (Cs - off-state) or a contact resistor (Rc - on-state); and a shunt coupling capacitor (Cg). Except Z0, other parameters are allowed to vary to fit the measurement results or the simulation results. The equivalent circuit is modeled by the QUCS (Quite Universal Circuit Simulator).
Zo
Rc
Rl
L
Zo
Ci Cg
Figure 5 The equivalent circuit model of lateral switch
According to equivalent circuit scheme, both S parameters and effect of each component over S-parameteres can be obtained and observed. S-Parameters:
Where
At the off-state of the switch, the switch capacitance, C s, is an important factor that affects the isolation of the switch. The isolation of switch can be approximately expressed as
-15 -20 -25 -30 s s L
o
-35 iot
n
s
e
r
-40 n I B
)
-45 (
d 1 S
2
-50 -55 -60 -65 0
2
4
6
8
10
12
14
16
18
Cs 0.1 fF to 20 fF
Figure 6 MatLab Results of Cs vs S21 at 5.8 GHz
Figure 7 QUCS Simulation of the model , Z 0 is 50 ohm at 5.8 GHz
20
Figure 8 Cs equals to 1 fF
Figure 9 Cs equals to 10 fF
As is it seen from the Figure 6, 8 and 9, S21 increases while Cs incereases. It means that isolation of a lateral switch has inverse proportion with Cs value. Additionaly, 5 dB difference is observed between MatLab and Qucs results, of course Qucs results are more realistic than Matlab results because qucs simulates the whole circuit where matlab uses only mathmetical S21 formula.
At the on-state of the switch, the insertion loss and the return loss can be expressed as:
Where
( ) ( ) ( ) | |
For on state, the insertion loss (S21) and the return loss (S11) of the switch can be simplified as:
Figure 10 R1 (Rl) and R2 (Rc) and Zo is 50 ohm
Figure 11 (Rl + Rc) equals to 0.2 ohm
Figure 12 (Rl + Rc) equals to 2 ohm
Figure 13 (Rl + Rc) equals to 5 ohm
As it seen from Figure 11, 12 and 13, the resistance sum ( Rl + Rc) should be as small as possible to achieve low insertion loss and high return loss. On the other hand, just mathmetaical formulas of s-parameters are cosidered, there is no frequency dependancy is observed but simulation results shows that inseriton and return losses have a frequency dependancy. The reason of this dependancy is caused from skin effect (depth) of metal layers. The skin depth is a measure of penetration of a plane electromegnetic wave into a material. The magnitude of the field in the material is proportional to where is skin depth, x is distance into the material from the surface where the wave is incident. In good conductor, skin depth is calculated by the formula:
⁄
⁄ ∑
Moreover, skin depth is the surface thickness of a metal at any frequnecy for which one skin depth (1 ) 63.2% of the current is flowing. For two skin depth 86.5% and for 4.6 skin depth 99% of the total current flows on a conductor’s surface. The surface resistivity (Rs) of the metal layer is given by
Where t is the metal thickness. Then, the resistance of a centilever beam (R l) can be expressed as
Where li and wi are the length and the width of different sections of the centilever beam. Therefore, the resistance of the centilever beam increases with frequency due to the skin effect. When the thickness and the conductivity of the metal layer are larger, the beam resistance is smaller so the RF Power dissipation decreases and the insertion loss of the switch is lower. Therfore, the
metal layer with high conductivity has to be coated as thickly as possible to achive good RF performance. The series inductance L can be calculated by
Where Zl is the impedance of the cantilever beam, l is the whole length of the cantilever beam is the phase constant, is the relative permitivity and c is the speed of the light in vacuum. Cg is the shunt coupling capacitance between the cantilever beam and the fixed electrode, which can be estimated as
-12
Where is the permitivity of the air (8.854 x 10 ), l2 is the lengt of the fixed electrode, h is the heighest of the cantilever beam, g 0 is the original gap distance between two electrodes, y is the displacement of the electrode part of the cantilever beam and Cf is the fringing filed capacitance which is 20-60% of Cg. This coupling capacitance is fairly large and affects the loss mechanism at the on state of the switch. The RF performance, including the insertion and return loss of the switch at the on state, are improved when Cg increases from 10 to 60 fF. It is noted that when the switch is actuated, the gap between the two electrodes, g (g0 – y) decreases. Hence, the coupling capacitance at on state is slightly larger than the one at the off state. On the other hand, the structure design of the cantilever beam and the distance between cantilever beam and the fixed electrode also determine the mechanical performance of the switch in terms of the threshold voltage and the switching speed. Therefore, it is important to select the proper values of l 2 and g0 for the switch design to compromise between electrical and mechanical performances.
Final Design:
In this design, A Si substrate is used with =11.7, H= 500 um and T=2 um parameters. The cantilever parameters are l1= 300 um, l2= 200 um, w1= 2.5 um, w2= 5 um and h= 50 um According to these parameters, the neccessary terms are calculated and simulated for on and off states at 5.8 GHz. Additonaly, Cu ( ) is used for metal coating.
∑ ( ) ( ) { }
According to Line Calculation Tool of Qucs, Zl impedance varies between 50 and 74.6 ohm because of the width of cantilever beam. Then;
√ Cs and Rc values are obtained by simulation or measurement. However, it is assumed that Cs = 1 fF and Rc = 1 ohm in this design.
Figure 14 Final Design for off-state
Figure 15 Off-State Results
Figure 16 Final Design for on state
Figure 16 On state results
1.2 MECHANICAL DESIGN AND SIMULATION The lateral switch is based on an elctrostatic actuator as shown in Figure 17. The actuator cosistis of for components. They are suspended cantilever beam serving as a movable electrode, anchor on the substrate to support the cantilever beam, fixed electrode opposite to the cantilever beam and contact bump.
Figure 17 The schematic of the top view of an electrostatic actuator
The cantilever beam OC is a beam mass structure. For the part of the beam OA, the width is w 1 and the length is l 1. For the part of the mass AC, the width is w 2 and the length is (l 2+l 3) in which l 2 is the length of the electrode section AB and l 3 is the length of the remaining part BC. The mass width, w 2, is designed to be relatively wider than the beam width, w 1, so that low threshold voltage can be maintained and greater deformation of the electrode section may be avoided.The original distance between the two electrodes is g0 and the distance between the contact bump and the mass part is d 0. d 0 is relatively smaller than g0 so that the cantilever beam can touch the contact bump when the switch is actuated. In Figure 17, the X - and Z -axes are oriented parallel to the length and the depth of the cantilever beam respectively, while the Y -axis is directed toward the fixed electrode. For the design of the lateral switch in static behavior, low threshold voltage is always desired. The threshold voltage is determined by two forces the electrostatic force (F e) and the restoring force (F r).
1.2.1 STATIC ELECTROSTATIC FORCE When a DC bias voltage (V ) is applied between two electrodes, the Electrostatic Force (F e) causes the mass to move toward the fixed electrode and the beam is bent. The bending of the mass part is negligible because it has much higher flexure rigidity than the beam. The displacement of the mass increases with voltage until pull-in occurs. If the displacement of the beam OA and mass AC from its original position are designated as y 1| x and y 2| x , respectively, the electrostatic force, F e, on the mass can be derived as
Where
∫ | | | | |
When the electrostatic force is not uniform, the bending moment (M0), caused by the electrostatic force can be calculated as
∫ (
) ( ) |
For small , Mo can be approximated as
The equation for the displacement of the beam y 1| x is determined
Where E 1 is Young’s modulus of the beam and l1 is the moment of inertia of the cross-sectional area of the beam. At x = 0, the boundary conditions are
| |
By solving the equations writtten above,
can be obtained as
Therefore, at a specific applied DC bias voltage V , F e, and M0 are determined by α and whereas α and are determined by M0 and F e. Thus, F e, M0, α and θ can be found through numerical iterations. For a voltage equal to or larger than a specific value, the iteration results become divergent. This specific voltage is called threshold voltage. For the threshold voltage, once α and are known, the displacement of he mass is found.
1.2.2 STATIC RESTORING FORCE
When the mass part is displaced, an elastic restoring force by the beam tends to pull the mass back toward its original position. At the end of the electrode part AB of the mass, the restoring force F r, can be written as
|
where k is the equivalent stiffness of the cantilever beam. Suppose that the mass is subject to a concentrated force at the midpoint of the electrode section, the equivalent stiffness, k can be expressed as
⁄
where E 2 is Young’s modulus of the mass and I2 is the moments of inertia of the cross-sectional area of the mass. Before the metal coating, the beam is merely made up of single-crystal silicon. E 1, E 2, I1, and I2 are given by
where E Si is Young’s modulus of the single-crystal silicon. After the metal coating,the beam is made of single-crystal silicon covered by metal on the top and sidewalls. Therefore, E 1, E 2, I1, and I2 can be expressed as
where E m is Young’s modulus of the metal, w m is the thickness of the metal coated at sidewalls of the silicon beam. Typically, w 1 = 2.5 –3 μm, w 2 = 5 –15 μm, w m ≤ 1 μm. Since E Siw 1 > 5E mw m, the equivalent stiffness is dominated by silicon structures. After the metal coating, the initial gap distance between two electrodes, g0, and the initial gap distance between the beam end and the contact bump, d 0, are expressed as
where gSi and d Si are the initial gap distance between the two silicon electrodes and the initial gap distance between the silicon beam and the silicon contact bump before metal coating, respectively.
1.2.3 STATIC THRESHOLD VOLTAGE
The balanced position of the cantilever beam can be found as the force is balanced F = F e + F r = 0 The curves of normalized F e and |F r| as functions of the normalized displacement y /g0 are shown in Figure 18. For a specific mechanical structure, k is a constant. Therefore, the curve for the restoring force, F r, is a straight line starting from the origin of the coordinates. The curve for the electrostatic force, F e, is a hyperbola. When the applied bias voltage, V , is less than a specific voltage V th, the two curves have two intersections. When the bias voltage V increases, F e increases and the two intersections move closer. When V = V th, the intersections coincide. When V > V th, the two curves do not intersect since F e =−F r at all displacements, that is, the mass part always collapses to touch the contact bump. V th is the threshold voltage, which can be calculated using the iteration method, as discussed in 1.2.1.
Figure 18 Normalized electrostatic force and restoring force on the movable cantilever beam with various applied bias voltages. [10]
The threshold voltage, V th, is determined by the cantilever beam structure and the original gap between two electrodes, g0. Figure 19 shows that the threshold voltage, V th, decreases when the original gap between the two electrodes g0 decreases or the length sum(l 1 + l 2) increases. When the
cantilever beam length ratio, l 2 / (l 1 + l 2) is within the range of 30 – 75 %, V th only changes within 10% of the minimum value of V th, which is referred to as [V th]min. The corresponding length ratio [l 2 / (l 1 +l 2)]min to [V th]min is 50% when w 1 = 2.4 μm, w 2 = 5 μm, and w Al = 0. It also shows that [l 2 / (l 1 + l 2)]min is almost independent of the initial gap, g0, and the length sum (l 1 + l 2). The effect of the metal thickness, W m, of sidewalls on the threshold voltage is more complicated. Initially when Wm increases from zero, the threshold voltage, V th, increases slightly. However, after the threshold voltage, V th, gets to its maximum value, it decreases with increase in Wm. This observation can be explained by two effects that arise from the metal coating at sidewalls. On the one hand, the metal increases the stiffness of the cantilever beam which tends to increase the restoring force, F r, and the threshold voltage, V th. On the other hand, the metal coating reduces the original gap between the two electrodes from gSi to (gSi –2W m), which tends to increase the electrostatic force, F e, and reduce the threshold voltage, V th. When Wm is small, the increase in F r dominates the increase in F e. As a result, V th increases. However, once Wm exceeds a specific value, the increase in F e dominates the increase in F r. Therefore, V th falls. In general, the change of the threshold voltage, V th, due to the metal coating is less than 5 V. (since Wm is less than 1 μm) 1.2.4 DYNAMIC FREQUENCY RESPONSE
The frequency response of the cantilever beam is useful to determine the switching time and the mechanical bandwidth of the lateral switch.
where (‘) denotes the derivative with respect to time t , y is the lateral displacement of the cantilever beam relative to the origin of the fixed electrode, m is the effective mass, k and b are the effective stiffness and the damping coefficient of the simplified system, and f ext(t ) is the electrostatic force. The electrostatic force, f ext(t ), between the two electrodes generated by a bias voltage, V , can be simplified as
Based on the Laplace transforms, the frequency response of the cantilever beam with small vibration amplitude can be expressed as
where ω is the working angular frequency, ω0 is the natural resonant angular frequency and Q is the quality factor of the cantilever beam. ω0 and Q are expressed as
The quality factor Q of the cantilever beam is determined by several different variables, such as the pressure, the temperature, and the intrinsic material dissipation. The quality factor is also an important component for the switching time. When Q ≤ 0.5, it has a slow switching time; when Q ≥ 2, it has a long settling time. In practice, it is beneficial for the switching time that the quality factor of the cantilever beam is designed by 0.5 ≤ Q ≤ 2. 1.2.5 DYNAMIC EFFECTIVE MASS
It is noted that the effective mass of the cantilever beam is not equal to the actual mass of the cantilever beam since only the end portion of the cantilever beam is moving. The effective mass, m, can be estimated by Rayleigh’s energy method. Assume the cantilever beam is subject to a concentrated load, P, at the center of the electrode section of the cantilever beam. We can consider the displacement yx and kinetic energy E k of the cantilever beam at three portions, respectively.
The first part of the beam is (0 < x ≤ l1), the second part of the beam is (l 1< x ≤l 1+l 2/2), the third part of the beam is (l 1 + l 2 / 2 < x ≤ l 1 + l 2 + l 3). Then the total kinetic energy is
where the velocity y max at the end of the cantilever beam is
|
The effective mass, m, can be obtained by solving the equations given above, it is obvious that the portion mass m1, m2 and the effective mass, m, of a cantilever beam changes with the ratio of (l 2/(l 1+l 2)).
Figure 19 Effective mass and part mass of the cantilever beam versus the ratio of l 2 /(l 1+l 2)
The effective mass, m, is mainly determined by the mass of the electrode part, m2. The effective mass, m, is 5 –85% of the actual total mass of the cantilever beam [m1 + m2(1 + l 3 /l 2)] when the ratio of [l 2/(l 1+l 2)] is within the range of 30 –75%. The natural resonant frequency of the cantilever beam changes with the ratio of (l 2/(l 1+l 2)) and the sum of (l 1+l 2). It shows that the natural resonant frequency of the cantilever beam changes slightly when l 2/(l 1+l 2) is within the range of 30 –75%.The natural resonant frequency of the cantilever beam decreases with the increase of (l 1+l 2) due to the increase of the effective mass and the decrease of the stiffness of the cantilever beam.
Figure 20 Natural resonant frequency versus the ratio of l 2 /(l 1+l 2)
Final Design:
The design whose parameters were determined in electrical design and simulation part is modeled with Comsol Multiphysics simulation program using FEM (Finite Element Method).
Figure 21 Comsol Model
For the structure of cantilever, eigenfrequency analysis is done. According to this analysis first five results are shown below.
Figure 22 First eigenfrequency at 9792.065 Hz
Figure 23 Second eigenfrequency at 84125.25096 Hz
Figure 24 Third eigenfrequency at 191.062 KHz
Figure 25 Fourth eigenfrequency at 217.221 KHz
Figure 26 Fifth eigenfrequency at 291.145 KHz eigenfunc.avi
Figure 27 Displacement vs. Voltage
Figure 28 Shape of cantilever vs. Applied Voltages
2.
CONCLUSION AND FUTURE WORK
As a conclusion, generally RF MEMS Switches are mentioned and then a rf mems lateral series switch is designed at 5.8 GHz and simulated by QUCS and Comsol Multiphysics computer programs in this study. When we compare our results to another switches can be found commercially in market, they are acceptable but cannot be substituted with them. For example:
The Design RF MEMS Switch [5] RF Switch [6]
S21 (Off-State) -50.5 dB -30 dB -27 dB
S21 (On-State) -1.77 dB -1.00 dB -0.50 dB
Table 4 Comparison of RF Switches
The main reason of the difference between results of mems switches are used substrate material and coating metal. Additionally, geometry and type of switches are also important parameters on the quality. As a future work, different geometries can be studied and more acceptable results might be get. Moreover, fabrication processes of switches can be also searched deeply and a fabrication process can be suggested. Finally, this study is really helpful for me to understand mems devices especially rf mems and switches.
