This paper presents the design, simulation and analysis of a 5-bit RF MEMS digital variable capacitor using thick SU-8 polymer to achieve both high capacitance ratio (\(\varvec{C}_{\varvec{r}}\)) and Q-factor. The proposed varactor design consists of five capacitive shunt switches loaded over a co-planar waveguide (CPW) line. This results 32 capacitance steps ranging from 102.23 fF to 3.57 pF (\(\varvec{C}_{\varvec{r}}\) = 35). The high capacitance ratio of the varactor is achieved by implementing SU-8 polymer as the base structure of the capacitor due to its low dielectric constant (\(\varvec{\varepsilon}_{\varvec{r}}\) = 4) hence reducing the overall minimum capacitance (\(\varvec{C}_{{\varvec{min}}}\)). The optimization of the SU-8 thickness has been carried out to get the optimum capacitance ratio and Q-factor. Moreover, the inclusion of semi-elliptical slot at the ground of CPW and variable sizes of CPW line further reduce the parasitic capacitance. To improve the reliability of the variable capacitor design, a new aluminium (Al) stopper design is used to prevent contact between the beams and the pull-down electrodes. Mechanical simulations and analysis have been carried out to investigate the effects of in-plane residual stress and stress gradient on the spring constant and the initial displacement of the proposed horizontal truss fixed–fixed beam structure. Compared to the conventional doubly clamped solid beam design, the proposed beam has less sensitivity to in-plane residual stress. This makes the pull in voltage to be less affected by the stress due to the fabrication. The simulated pull-in and lift-off voltages are 30 and 25 V respectively while the estimated switching time for the beam is 4.64 μs. The overall size of the varactor is 740 μm × 653 μm. The proposed RF MEMS varactor could be integrated in reconfigurable filters, phase shifters and matching networks targeting future multi-standard wireless communication systems.
1 Introduction
Due to rapid development in wireless communication in recent years, a lot of research have been carried out to realise multiband and reconfigurable front-end components to deal with ever increasing wireless communication standards. In order to support these standards such as GSM, WiFi, LTE, and Bluetooth, low power and compact size devices are required. In the RF transceiver part, tuning and reconfigurable elements such as tunable filters, matching networks and phase shifters play an important role to support these bands without increasing its overall size. Variable capacitors are one of the key components used in these systems. Commercially available solid-state varactors such as p-n junction diodes and Schottky diodes offer wide tuning range, small size and very fast tuning speed (Rebeiz 2003; Reinke 2011). However, they suffer from low power handling, low Q-factor, non-linearity effect, and high loss especially at high frequency bands. With the advent of the microelectromechanical systems (MEMS) technology, MEMS based varactors are seen as the best candidates to replace the solid-state varactors. The main advantages of MEMS varactors over the conventional solid-state technology are low loss, zero power consumption (electrostatic actuation), high-Q factor and high linearity with respect to RF power (Gupta et al. 2013; Reinke 2011). In general, there are two types of MEMS varactors: analog and digital. Various analog and digital MEMS designs have been demonstrated in the literature (Gupta et al. 2013; McFeetors and Okoniewski 2007; Patel and Rebeiz 2012; Reinke 2011). One of the limitations that hampers the performance of analog designs is its low tuning ratio which is important to obtain wider tunability characteristic due to pull-in effect. This phenomena can be explained by the mechanical instability between electrostatic forces and restoring forces of the varactor structure, which causes the metal bridge to snap down when it reaches one-third of the air gap (Gupta et al. 2013; McFeetors and Okoniewski 2007). One way to achieve higher capacitance range is by employing digital type MEMS varactors or switched capacitor banks (Bakri-kassem 2007; Dussopt and Rebeiz 2003). Digital MEMS varactors are formed by several switches loaded on a transmission line where the capacitance values are selected by switching ON and OFF the switches. The capacitance ratio of digital varactors can be calculated by finding the ratio of the maximum and minimum capacitance values obtained when all switches are in ON states and OFF states respectively. However, the capacitance ratio of the digital design is still limited by a high minimum capacitance (Cmin) value originating from the fringing field and parasitic capacitance between the silicon substrate and coplanar waveguide.
SU-8 is a polymer that is widely used in MEMS devices especially for MEMS sensor as photo-resist sacrificial mask and to construct high aspect ratio structure (Melai et al. 2007) due to its thermal and chemical stability in the fabrication process. Recently, SU-8 was used as a passivation layer to elevate co-planar waveguide (CPW) for realising a low loss transmission line using low resistivity silicon wafer (ρ < 100 Ω cm). (Lucibello et al. 2013; Marcelli et al. 2008) had used SU-8 as a lateral support for RF MEMS switch and sacrificial layer. Our previous work reported that by depositing and patterning 25 µm thick SU-8 layer on a silicon substrate, the parasitic capacitance due to fringing field and loss of the varactor could be reduced, hence increasing the capacitance ratio and the Q-factor of the proposed RF MEMS varactor (Ramli et al. 2016a, b). In this paper, an optimisation of the SU-8 layer thickness has been carried out to produce the optimal value of the capacitance ratio and the Q-factor. In addition, mechanical simulations have been conducted using the finite element method (FEM) software, CoventorWare™ to investigate the effects of in-plane residual stress and stress gradient on the spring constant and the initial displacement of the beam structure. A comparison between the proposed truss fixed–fixed beam design and conventional solid beam in terms of pull-in voltage and their tolerance towards in-plane stress and stress gradient is presented.
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2 Design of the RF MEMS varactor
Digital MEMS varactors operate as a typical MEMS capacitive switch based on mechanical movement in lateral or vertical direction to achieve ON and OFF states (Rebeiz 2003). Normally, they are made of an array of shunt switches suspended over the centre conductor of a co-planar waveguide (CPW). Both ends of the switches are fixed to the ground to realize a digital varactor design. The bottom electrode under the beam provides the electrostatic actuation while RF capacitance is created between the suspended beam and the transmission line. The minimum capacitance is obtained when all the switches are in the upstate position; while the maximum value is achieved when all the beams are pulled down. The minimum capacitance during upstate condition, \(C_{u}\) can be calculated as
where ɛ0 = 8.854 × 10−12 is the permittivity of free space, A is the contact area of the both plates, g0 is the initial gap, \(t_{d}\) is the dielectric thickness, and ɛr is relative dielectric constant. Typically, additional fringing field, Cf will contributes around 20–60% of the overall capacitance when the switch is on upstate position (Ramli et al. 2016a, b; Rebeiz 2003). The maximum capacitance of the varactor in the downstate position, Cd is given by
Figure 1 presents the top view of the proposed digital variable capacitor. The design consists of 5-bit binary weighted capacitive shunt switches over a co-planar waveguide (CPW) transmission line. The binary weighted capacitance values are calculated by varying the contact areas between the centre conductor of the CPW line and the bridges using (1) and (2).
Fig. 1
5-bit RF MEMS digital varactor
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The RF MEMS varactor is developed to achieve a high tuning range and Q-factor by utilising SU-8 technology. The parasitic capacitance is reduced by elevating the varactor from the silicon substrate by spin-coating the substrate with SU-8 layer as shown in Fig. 2, thus greatly increasing its tuning range. The thickness of SU-8 layer (tsu-8) was varied from 0 to 30 µm in order to obtain the optimal capacitance ratio and Q-factor. Apart from that, SU-8 is also used as the lateral support for the beams of the varactor. To improve the power handling of the design, a novel horizontal truss aluminium beam with thickness of 2 μm is proposed as shown in Fig. 3.
Fig. 2
Side view of the MEMS varactor
Fig. 3
a Top view of side pull-down and stopper with the beam. b Side pull-down and stopper underneath the beam
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One of the major failures of RF MEMS varactors is stiction due to dielectric charging effects. One of the effective ways to prevent this issue is to separate RF and DC electrodes for the switch actuation. As such, to increase the reliability of the varactor, a side pull-down configuration and a new stopper design is implemented. The detailed design of the stopper is shown in Fig. 3. A gap of 0.5 μm that exists between the actuator pad and the top beam in the downstate position would prevent direct contact between them. The semi-elliptical at the ground as shown in Fig. 1 further reduces the parasitic capacitance slot. The summary of the proposed design parameters is shown in Table 1.
Table 1
Detailed dimensions of the digital varactor
Symbol
Description
Value
L
Length of the beam
550 µm
g0
Air-gap
3.1 µm
td
Thickness of dielectric layer
0.25 µm
ɛr1
Relative permittivity of dielectric layer
7.5
t
Thickness of the beam
2 µm
wt
Width of the truss beam structure
5 µm
ts
Silicon substrate thickness
525 µm
ρ
Resistivity of silicon substrate
10 k Ω m
W
Width of the co-planar waveguide transmission line
80 µm
G
Gap of the co-planar waveguide transmission line
50 µm
A1
Area of bit-1 of the varactor
10 µm × 40 µm
A2
Area of bit-2 of the varactor
20 µm × 40 µm
A3
Area of bit-3 of the varactor
40 µm × 40 µm
A4
Area of bit-4 of the varactor
80 µm × 40 µm
A5
Area of bit-5 of the varactor
160 µm × 40 µm
tSU-8
Thickness of SU-8 layer
0, 5, 10,15, 20, 25, 30 µm
ɛr2
Relative permittivity of SU-8
4
tan δSU-8
Loss tangent of SU-8
0.04
Ael
Area of pull-down electrode
1.82 × 10−9 µm2
E
Young’s modulus of aluminium
69 GPa
Vp
Pull-down voltage
30.31 V
Vh
Holding voltage
25 V
kT
Spring constant
1.33 N/m
Cd(max)
Maximum capacitance value
3.57 pF
Cu(min)
Minimum capacitance value
102.23 fF
Cr
Capacitance ratio
35.7
3 Results and discussions
The proposed MEMS varactor design has been simulated in CST Microwave Studio to evaluate and analyse its RF characteristics. Optimisation of SU-8 layer thickness has been done by varying its thickness to achieve two main goals which are high capacitance ratio and improved Q-factor. On the other hand, the mechanical analysis of the beam structure was conducted via CoventorWare™.
3.1 Electro-magnetic simulations
A high resistivity silicon substrate, σ = 0.01 S/m (ρ = 10 k Ω cm) was used to improve the RF performance of the proposed varactor. Based on the Smith chart in Fig. 4, capacitance values and the Q-factor of the varactor can be extracted from the S11 plot using Eqs. (4) and (5) (Rebeiz 2003)
$$C = - \frac{1}{2\pi fX},$$
(4)
$$Q = \frac{{Im (Z_{in} )}}{{Re(Z_{in} )}}$$
(5)
Fig. 4
Simulated S11 of the MEMS varactor from 0 to 10 GHz a state 1 (all beams on upstate), b state 32 (all beams on downstate)
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The optimal thickness of the SU-8 layer was achieved by comparing the capacitance ratio and the Q-factor for seven different thickness values which are 0, 5, 10, 15, 20, 25 and 30 µm. The simulated results of the respective thickness are tabulated in Table 2. It can be seen that by increasing the thickness of the SU-8, the capacitance ratio of the varactor increases. However, the maximum capacitance ratio is obtained when the thickness is 20 µm while by placing the varactor directly on the silicon substrate results in the lowest capacitance ratio. This is due to less fringing field between the varactor and the SU-8 due to its lower dielectric constant compared to silicon. Q-factor of 812 and 50 were achieved for the Cu(min) and the Cd(max) respectively for the thickness of 20 µm. This shows that good RF performance could also be realised by using thick SU-8 as the passivation layer.
Table 2
Capacitance ratio and Q-factor for different thickness of SU-8
Thickness (µm)
Capacitance ratio
Q-factor (upstate/downstate)
0
16.9
248/95
5
24.5
505/114
10
28.9
613/108
15
34.4
762/93
20
34.8
812/50
25
34.6
648/66
30
33.5
827/62
The power handling capability of the varactor is calculated by simulating the pull-in voltage, Vp between the beam and the centre conductor for the largest bit switch since the RF power is induced on the centre conductor. The maximum RF power before self-actuation is calculated using Eq. (6) (Rebeiz 2003).
$$P = \frac{{V_{p}^{2} }}{{Z_{0} }}$$
(6)
where P is the incident RF power, Z0 is the characteristic impedance of the line. In addition, the dielectric strength of SU-8 is 4.43 ± 0.16 MV cm−1 which is remarkably high for a polymer material. It is reported that for 15 μm thick SU-8 has voltage breakdown of around 7 kV and increases over the thickness (Melai et al. 2009). The simulated pull-in voltage Vp from the centre conductor is 10.5 V and the calculated maximum RF power is 2.2 W. There are 32 capacitance steps which change linearly from 102.23 fF to 3.57 pF with an incremental capacitance step of 0.11 pF as demonstrated in Fig. 5.
Fig. 5
32 capacitance steps of the variable capacitor
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3.2 Mechanical simulations
The structure of the truss beam as shown in Fig. 1 was analysed using CoventorWare™ to calculate the pull-in and the holding voltage. In order to obtain similar pull-in voltage for all beams, the beam width is fixed at 50 µm. All the five beams were simulated to calculate their pull-in voltage. The side pull-down pads were implemented to separate the DC voltage and RF voltage to reduce dielectric charging. An incremental positive bias voltage was applied at the pull-down pads while DC potential of the beam is kept at 0 V. The simulated pull-in voltages are within the range of 28–32 V. The discrepancies are mainly due to different sizes of the centre structure of the beams. On the other hand, the lift off or holding voltage analysis was conducted by decreasing the voltage from pull-in voltage until the beam was released to its initial up-state position. Figure 6 shows the pull-in voltage for the 80 µm centre width beam is 30 V while its holding voltage is 25 V. The beam deformation during pull-in voltage is shown in Fig. 7 and the red colour in the centre of the beam determines the maximum displacement. The displacement value of 1.8 µm is more than the one-third of the gap height indicating that mechanical instability had occurred and the beam was pulled down. To investigate the effects of in-plane residual stress and stress gradient on the beam, different values of both stresses were simulated. Generally, the biaxial residual stress introduced on the MEMS structure is due to fabrication process. In this work, in-plane residual stress of 0, 50 and 100 MPa were chosen to analyse its effect on the spring constant of the proposed beam (Reines et al. 2009; Yang et al. 2014). As comparison, a solid fixed–fixed beam of similar configuration (length = 550 µm, width = 50 µm and t = 2 µm) was also analysed. The sensitivity analysis due the residual stress for both beams was carried out. In addition, vertical stress gradients of 0 to ±8 MPa/µm were induced on the beam structure to analyse its initial displacement. Further analysis will be discussed in Sects. 3.3.1 and 3.3.2.
Fig. 6
Pull-in voltage and hold in voltage for 80 µm beam
Fig. 7
Beam displacement when the pull-in voltage applied
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3.3 Modal analysis
Modal analysis of the beam varactor was carried out to compute the mechanical natural frequencies of the structure at equilibrium. The calculated frequencies and their associated mode shapes are shown in Fig. 8. The finding of these frequencies helps to understand how the beam would respond to the surrounding noise. The resonance frequencies of the 80 µm beam is at 53.9, 110.5 and 142.8 kHz. These resonances occur without any external force applied to the beam structure. In addition, the switching speed of the beam can be estimated by one-quarter period of the mechanical primary natural frequency of the beam (Goldsmith et al. 1999). This results the theoretical switching speed of 4.64 µs.
Fig. 8
Mechanical resonant frequencies of the beam at a 53.9 kHz, b 110.5 kHz and c 142.8 kHz
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3.3.1 In-plane stress
The total spring constant, kT of a mechanical beam is given by the summation of spring constant due to mechanical properties of the beam, k1 and stress-induced spring constant after fabrication process, k2. The total spring constant is then calculated as
$$k_{T} = k_{1} + k_{2}$$
(7)
The spring constant of the beam is calculated by finding its pull-in voltage and using equation (Rebeiz 2003)
The total spring constant of the beam without residual stress is 1.33 N/m while for the solid beam design is 4.88 N/m. The corresponding pull-in voltages are 30.31 and 58.2 V respectively. This shows that the proposed beam can reduce the actuation voltage by almost 50%. The advantage of the truss beam over conventional solid beam design could be further emphasised by comparing its sensitivity to in-plane residual stress. Both designs were simulated with in-plane residual stress of 0, 50 and 100 MPa. The simulated spring constants against residual stress are shown in Fig. 9. It can be seen that the spring constant of the truss beam increases by only 3 N/m for a residual stress of 50 MPa which results in a maximum k2/k1 ratio of 2.6 as shown in Fig. 10. As comparison, the solid beam structure will result in a k2/k1 ratio of 5 demonstrating its higher sensitivity to in-plane residual stress.
Fig. 9
Simulated spring constant versus in-plane stress
Fig. 10
k2/k1 ratio versus in-plane stress
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3.3.2 Stress gradients
The beam structure was also simulated versus varying vertical stress gradients. The deformation of the centre plate along the beam length direction due to vertical stress gradient of 0 to ±8 MPa/µm are shown in Fig. 11. The simulation results show that positive stress gradients cause the beam to deflect downward while negative stress deflect the beam in the opposite direction. A stress gradient of ±8 MPa/µm will result in maximum centre displacement of 0.3 µm which is still within the acceptable range (Reines et al. 2009).
Fig. 11
Simulated displacement in the centre plate of the truss beam versus vertical stress gradient
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3.3.3 Von Mises stress
Further simulation on the von Mises stress was undertaken in order to investigate the stress on the beam during actuation. This analysis is important to ensure the beam structure can withstand the maximum applied force. Figure 12 shows that the maximum von Mises stress is located at the end of the beam. These values are lower than the yield strength of aluminium (124 MPa) and gives a clear indication that the beam would not break when actuated.
Fig. 12
Von Misses stress for truss beam
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4 Proposed fabrication process
Below are the overview of the proposed fabrication process for the varactor design. The fabrication process of the MEMS varactor composes of several steps described using the following diagram in Fig. 13. A 525 µm thick high resistivity silicon wafer is chosen as the substrate. A total of five masks are required for the fabrication process. First, 20 µm of SU-8 is spin-coated on the surface of silicon wafer. Then, the SU-8 is soft baked to evaporate the solvent before it can be exposed under the UV light. Next, post exposure bake (PEB) is performed. To further cross-link and cure the SU-8 layer, hard bake is needed at temperature 210 °C for 1 h. As a precaution, the SU-8 cannot be baked at a very high temperature (exceeding 300 °C) to avoid crack in the film and it must be more than subsequence process temperature to make it withstands the temperature. As for this process, the subsequence process must not exceed 200 °C. After curing the SU-8, 2 µm of thickness of Al is sputtered and patterned using dry etching process to form the CPW transmission lines and stopper. In the next step, 1.5 μm Al is deposited and patterned using lift-off process to define the side pull-down electrode. Then, thin tantalum nitride (TaN) is patterned by lift-off process to form the bias lines after deposition. By using plasma enhanced chemical vapour deposition (PECVD) technique, 2500 Å Si3N4 is patterned on top of the centre conductor, stopper, and pull-down electrode as dielectric layer. In this process, 150 °C instead of 300 °C for plated shower is used to make sure it will not affect the SU-8 layer. Next, around 7 μm thickness of polymer or any sacrificial layer such as SU-8 or polyimide is spin coated and cured up to 200 °C to form the anchor and sacrificial layer (Lucibello et al. 2013). Adhesion between the sacrificial layer material and SU-8 is needed to be taken to account. Common sacrificial layer such as silicon oxide is not suitable for this work due to poor adhesion to the SU-8. Then, chemical mechanical polishing (CMP) technique is then used to level the SU-8 to get around 5.35 µm for the anchor and sacrificial layer. Then, 2 μm Al is deposited and patterned to form the beam and ground. The sacrificial layer then will be removed using oxygen plasma to release the beam.
Fig. 13
Proposed fabrication process of the devices. a High resistivity silicon. b Spin coat of SU-8. c Deposit and pattern of Al for CPW and stopper. d Deposit and pattern of Al for pull-down electrode. e Deposit and pattern TaN for bias line. f Deposit and pattern Si3N4 for dielectric layer. g Deposit sacrificial layer and CMP. h Remove sacrificial layer. Gray rectangle Si, red rectangle SU-8, yellow rectangle Al, light green rectangle TaN, dark green rectangle Si3N4,pink rectangle sacrificial layer
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5 Conclusion
This paper has presented the design, simulation and analysis of a 5-bit RF MEMS varactor for wireless applications. In this paper, thick SU-8 polymer has been implemented as a base structure to elevate the varactor from the silicon substrate to achieve high capacitance ratio. The thickness of the SU-8 layer has been optimized using simulation tool in order to get the optimum capacitance ratio and Q-factor which is 35 and 812 respectively. Besides that, the advantages of the truss beam structure over conventional doubly clamped solid beam design has been analysed and highlighted in terms of spring constant, pull-in voltages, in-plane stress and gradient stress effects. The proposed truss beam has shown it can reduce almost 50% of actuation voltage from solid beam and has less sensitivity to in-plane stress during the fabrication. The proposed varactor design could be applied to reconfigurable and multi-band RF front end components such as tunable filters, impedance matching networks and phase shifters.
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