1 Introduction

Radio frequency micro-electromechanical switches (RF MEMS) have a much better performance at high frequencies compared to similar ones, including FET switches and p-i-n diode switches. The advantages of these switches include low power consumption, high cut-off frequency, high electrical isolation in all frequency bands, small size and low weight [1, 2]. MEMS switches can be divided into several types based on the type of actuation (electrostatic, electromagnetic, electrothermal and piezoelectric), circuit configuration (series or parallel), and the type of connection to the transmission line (capacitor or metal-to-metal). Discussion on these cases and the choice of an optimal switch was done in [3, 4].

One of the disadvantages of RF MEMS switches is the high actuation voltage, low power transmission and high stress on the beam after the switch actuation. Each of these can significantly reduce the lifetime of the switch. In recent years, many works have been done to eliminate the actuation voltage problem, including increasing the cross-section, reducing the hardness of the spring and reducing the initial gap [5]. In addition, to reduce the amount of stress applied to the beam after the actuating of the switch, one can use the step structure in the beam and the two-height spring with elasticity in the vertical direction [6].

RF MEMS switches have been extensively used in space and military industries due to low power consumption losses of almost zero over the past two decades, and therefore improving the performance of these switches is considered very important. Furthermore, these systems are very suitable for use in radar, cell phone, Bluetooth and Wi-Fi applications in the frequency range of 30 kHz–300 GHz [3, 4, 7].

Following the improvements made to micro-electromechanical systems over the past twenty years, switches with the excellent characteristics and parameters in recent years are simulated. The results of some of the simulation of these switches are as follows:

In [8], three structures with low spring coefficients were proposed to reduce the actuation voltage of the switch. These switches are used in circuits in series. The actuation voltage for these structures varies between 6 and 14 volts, and the good RF specifications include an isolation of − 70 dB to − 76 dB and an insertion loss between 0.005 and 0.06 dB at a frequency of 10 GHz. A capacitive RF MEMS switch was fabricated using two high-impedance transmission lines in [9]. One of the advantages of this switch is to eliminate the surface roughness by presenting a new manufacturing method, which results in a good S-parameter. For this switch, the actuation voltage is equal to 20 V. In addition, the results obtained after RF analysis demonstrate better isolation than 18 dB and return loss less than − 20 dB in the C-K band. Given that in the manufacture of MEMS switches, the stiffness coefficient is usually higher than 10 N/m, but the three switches fabricated in [10] have a stiffness coefficient of 1.34–1.56 N/m. This reduction in the spring-stiffness coefficient leads to a decrease in the actuation voltage of about 4.8–6.3 V. In addition, for these three structures, the best isolation was 40 dB at 17 GHz and the best insertion loss was 0.25 dB at 20 GHz. A single membrane switch with a 4.3 V actuation voltage was fabricated in [11]. This switch has good RF characteristics, including a 36 dB isolation and an insertion loss of 0.52–2.05 dB at a frequency of 20 GHz.

In this paper, at first three switches fabricated in [10] are exactly simulated and then, the results of this simulation are compared with the results of the fabrication. The purpose of this comparison is to demonstrate the high quality and credibility of simulations. Then, some of the parameters of the three basic switches are optimized in four steps. These parameters included stress, switching time, actuation voltage, and isolation.

2 The common structure of an RF MEMS switch

In RF MEMS switches a microstrip line or Coplanar Waveguide (CPW) line on the substrate are typically use, which is preferable to microstrip due to easier access to ground plates. Capacitive switches are often used in circuits with parallel configurations. The difference in parallel and series configuration is in capacitor coupling in determining the operating frequency of the switch. In the parallel configuration, the switch has the ability to function up to 200 GHz, while in the series configuration this ability reduces to 20 GHz. Another advantage of capacitive switches is the insertion of a dielectric layer between the beam and the transmission line, which prevents the switch from direct contact with the membrane and the transmission line and increases the lifetime of the switch in the high number of cycles. The schematic diagram of the MEMS capacitive switch in up and down states is shown in Fig. 1a and Fig. 1b, respectively. As shown in Fig. 1b, after applying the voltage to the beam, the RF input and output are connected to each other and the switch is in the on state. To obtain the voltage required to actuate this switch, one can use Eq. 1:

$$V_{pull - in} = \sqrt {\frac{{8 k_{T} g_{i}^{3} }}{{27 \varepsilon_{0} A}}}$$
(1)

where \({\text{V}}_{{{\text{pull}} - {\text{in}}}}\) is the actuation voltage, \({\text{g}}_{\text{i}}\) the initial gap between the beam and the dielectric, \(\varepsilon_{0}\) the permeation coefficient of the vacuum and A the cross-sectional of the overlap area. It should be noted that for the design of a MEMS switch, the transmission line impedance must be equal to 50 Ω. The impedance of the transmission line depends on the substrate and switch type, the gap between the transmission line and the ground, the width of the transmission line and the height of the substrate. The electrical model of an RF MEMS capacitive switch is illustrated in Fig. 1c.

Fig. 1
figure 1

Side view of the switch in (a) up state (off), (b) down state (on), (c) electrical model of the switch

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One of the most effective parameters to improve the RF performance is the high capacitive ratio, which requires a maximum capacitor in the down state and a minimum capacitor in the up state. Equations 2 and 3 can be used to obtain the down state and up state capacitors, respectively. As seen in these Equations, the gap change will lead to fundamental changes in the value of the up state capacitor. In addition, the capacitance ratio of the switch can be calculated using Eq. 4. By increasing the capacitive ratio of the switch, excellent RF performance can be achieved, resulting in high isolation and low losses.

$$C_{down} = \frac{{\varepsilon_{0} \varepsilon_{r} A}}{{t_{d} }}$$
(2)
$$C_{up} = \frac{{\varepsilon_{0} A}}{{g_{i} + \frac{{t_{d} }}{{\varepsilon_{r} }}}}$$
(3)
$${\text{CR}} = \frac{{C_{down} }}{{C_{up} }} = \frac{{\frac{{\varepsilon_{0} \varepsilon_{r} A}}{{t_{d} }}}}{{\frac{{\varepsilon_{0} A}}{{g_{i} + \frac{{t_{d} }}{{\varepsilon_{r} }}}}}}$$
(4)

where \(t_{d}\) and \(\varepsilon_{r}\) are the thickness and the coefficient of the dielectric, respectively. Another important parameter in MEMS switches is the type of material used as a beam, which has a great effect on isolation and switching time. The material used as a beam should have a high electrical conductivity to achieve good isolation. It also needs a small mass density to increase the resonance frequency according to Eq. (5). By increasing the resonance frequency, according to Eq. 6, the switching time will decreases and the switching speed increases.

$$\omega_{0} = \sqrt {\frac{k}{{m_{eff} }}}$$
(5)
$$t_{s} = \frac{{3.67 V_{p} }}{{V_{s} 2\pi f_{0} }}$$
(6)

where \(\omega_{0}\) is the resonance frequency, k the spring-stiffness coefficient, meff the effective mass of the beam, ts the switching time and \(V_{s} = 1.4V_{p}\). The following equations can be used to obtain the Sparameter:

$$S_{11} = - 20\log \left| {\frac{{ - Z_{h} }}{{2Z_{h} + Z_{0} }}} \right|$$
(7)
$$S_{21} = - 20\log \left| {\frac{{2Z_{h} }}{{2Z_{h} + Z_{0} }}} \right|$$
(8)

where Z0 is the impedance of the CPW line and Zh the impedance of the MEMS bridge.

3 Comparison of simulation and fabrication results

In this section, first three designed and fabricated switches in [10] are introduced. As shown in Fig. 2, three switches with different structures are fabricated by Shekhar et al. In Table 1, the results of the fabrication of the three switches are considered. As can be seen, these results are very suitable. In order to demonstrate the high credibility of the simulations, the same three switches are simulated and the results are compared with the results of the fabrication of these switches. As shown in Fig. 3, the results of the simulation are very close to the results of the fabrication, which indicates the credibility and high quality of the simulations.

Fig. 2
figure 2

Schematic of the three switches fabricated in [10]

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Table 1 The results of the fabrication of the three switches presented in [10]
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Fig. 3
figure 3

Comparison of S-parameter for basic structures in fabrication and simulation (a) first structure (b) second structure (c) third structure

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4 Design and simulation of new switches

4.1 The main structure

To improve the results of the switches fabricated in [10], the original structure of the three switches was changed and three new switches were introduced using the new spring structure. As discussed in the previous section, the simulations presented in this paper are based on fabrication, and the same results will be obtained from simulations if three new switches are fabricated. Three new structures with their dimensions are shown in Fig. 4.

Fig. 4
figure 4

Top view of three proposed switches with their dimensions (a) first design (b) second design (c) third design

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4.2 Effect of holes on the switch parameters

By placing several holes inside the membrane, the mass of the switch is reduced, which, according to Eq. 5, increases the resonance frequency, thereby reducing the switching time. In addition, after applying force when the beam is pulled down, the air below holes goes out, which will make the pull-in and pull-up process easier to switch. But, there is a disadvantage in creating holes. By creating holes, the area of the cross-section of the switch decreases. As a result, the input signal is transmitted from the lower cross-section to the ground and the isolation decreases. To better understand this, one can refer to [3, 4].

4.3 The effect of changing the thickness of the beam on the switch

The switching time can be calculated using Eq. 6 and the releasing time can be evaluated using the following equation:

$$t_{pu} = \frac{1}{{4 f_{0} }} = \frac{\pi }{2}\sqrt {\frac{{m_{eff} }}{k}}$$
(9)

where f0 is the resonant frequency of the switch and tpu the releasing time. The time that lasts the beam reaches the dielectric is ts and the time duration that the beam returns to its original state is tpu. Using the COMSOL software, the first three modes of resonance frequency for each structure are shown in Fig. 5. As seen, only the first mode matches with our expectation of the behavior of the MEMS switch. As a result, for three proposed switches, the resonant frequency is 21 kHz, 32 kHz and 26 kHz, respectively. In Table 2, the physical characteristics of the proposed switches are given. In addition, in Fig. 6, the releasing and switching times are compared for different beam thicknesses.

Fig. 5
figure 5

The first three modes of the resonance frequency (a) first design (b) second design (c) third design

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Table 2 Physical characteristics of the proposed Switches
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Fig. 6
figure 6

Comparison of (a) the switching time and (b) the release time of the three proposed switches for different beam thicknesses

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4.4 The actuation voltage and design of the spring structure

In Fig. 4, the spring structure of the designed three switches with their dimensions is seen. To obtain the spring-stiffness coefficient, we can use Eqs. 10 and 11:

$$K_{1,2,3 \ldots } = \frac{{EWt^{3} }}{{L^{3} }}$$
(10)
$$\frac{1}{{K_{x} }} = \frac{1}{{K_{1} }} + \frac{1}{{K_{2} }} + \frac{1}{{K_{3} }} + \cdots$$
(11)

where E is Young’s modulus and W, t, and L the width, thickness, and length of each part of the spring, respectively. Given that in each of these structures four springs are used, according to Eq. 12, the stiffness coefficient of the total springs used in the switch is obtained as:

$$K_{T} = 4 \times K_{x}$$
(12)

4.5 Comparison of RF characteristics in Optimized Switches with Basic Switches

In the previous section, the optimization procedure of the switch using a new spring structure for each design was described. The switches fabricated in [10] uses Si3N4 as a dielectric layer. Simulations show that RF performance is improved by using a higher-coefficient of the dielectric. Therefore, in new designs, AlN is used as a dielectric layer, whose dielectric coefficient is higher than Si3N4, and it is also a hard material. Dielectric hardness is important due to the fact that it prevents the bulge and erosion in the high number of cycles during collision of the beam to the dielectric, which increases the lifetime of the switch. Figure 7 illustrates the isolation comparison for the proposed structures with the basic structures.

Fig. 7
figure 7

Comparison of the isolation between the initial structures and the proposed structures (a) first design, (b) second design, (c) third design

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5 Results and discussion

The fabricated switches in [10] are optimized in four steps, which are discussed below:

5.1 Reduction of the actuation voltage

According to Eq. (1), there are three ways to reduce the actuation voltage: First way is to decrease \(g_{i}\), the second way is to decrease K and the third one is to increase A, which is the best way to reduce the spring-stiffness coefficient [3, 4]. In this paper, three new structures for spring have been used to reduce the actuation voltage in a way that it reduces the stiffness of the spring. In addition, as far as possible, the gap between the beam and the dielectric has been reduced so that the self-actuation phenomenon and the degradation of the capacitive ratio do not occur.

5.2 Increase of the isolation

The choice of dielectric type is important for high isolation. In this paper, AlN has been used as a dielectric layer for all three structures, which has a high dialectic coefficient and it is considered a hard material, which results in a longer lifetime of the switch in a long time. Table 3 shows the value of the S-parameter and the actuation voltage for the new structures.

Table 3 The results of the simulation of the three proposed switches
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5.3 Reduction of the stress

After applying force to the beam, stress is applied to places where the springs are attached to the ground. This stress has a negative effect on the switch function and its lifetime in the high number of cycles. As shown in Fig. 8, the amount of stress applied to the switches fabricated by Shekhar et al. [10] is far greater than stress on the switches proposed in this paper. To compare stress in these springs, a same force is applied to the point of attachment of the springs to the beam. Then, the stress range is considered between 0 and 12 MPa for all springs. This stress reduction is achieved using the designed spring structure in new switches.

Fig. 8
figure 8

Comparison of stress between (a) switches fabricated by Shekhar et al. [10]. b The proposed switches

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5.4 Reduction of the switching time

As explained before, reduction of the switch mass can decrease the switching time. In this paper, the mass of the switch is reduced using a few holes inside the beam. But another way to reduce the mass of the switch is to use a substance with a mass less than aluminum. Beryllium is an excellent metal for the beam, because in addition to its low mass density, it has an electrical conductivity close to the aluminum, and in this way, it keeps the isolation of the switch in the desired range. To prove this claim, the switching times for the new structures using aluminum and beryllium are compared in Fig. 9. Also, Fig. 10 shows the isolation for new structures using these two materials. As it is seen, the switching time is significantly improved, which is an excellent advantage, and the isolation, although is reduced, is still excellent.

Fig. 9
figure 9

Comparison of switching times for two materials of aluminum and beryllium in three proposed structures

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Fig. 10
figure 10

Comparison of the isolation in the three proposed structures for the aluminum and beryllium switch

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The switches designed in this article are compared with the previous works, the result of which is given in Table 4. It is clear that the results of this design are great compared to many previous works.

Table 4 Comparison of the proposed switches with previous work
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6 Conclusion

In this paper, the three basic structures were considered, and then, some important parameters of the switch including actuation voltage, switching time, stress and isolation are optimization in four steps. The lifetime of the switches was also increased by changing the type of Si3N4 to AlN, using a new spring structure. According to the results, actuation voltage and stress are reduced 50% and 65% after the completion of the optimization steps, respectively. Also, the isolation is increased by 16%.