Circuit Modelling and Eigenfrequency Analysis of a Poly-Si Based RF MEMS Switch Designed and Modelled for IEEE 802.11ad Protocol

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  • ABSTRACT

    This paper presents the equivalent circuit modelling and eigenfrequency analysis of a wideband robust capacitive radio frequency (RF) microelectromechanical system (MEMS) switch that was designed using Poly-Si and Au layer membrane for highly reliable switching operation. The circuit characterization includes the extraction of resistance, inductance, on and off state capacitance, and 𝚀-factor. The first six eigenfrequencies are analyzed using a finite element modeler, and the equivalent modes are demonstrated. The switch is optimized for millimeter wave frequencies, which indicate excellent RF performance with isolation of more than 55 dB and a low insertion loss of 0.1 dB in the V-band. The designed switch actuates at 13.2 V. The R, L, C and 𝚀-factor are simulated using Y-matrix data over a frequency sweep of 20–100 GHz. The proposed switch has various applications in satellite communication networks and can also be used for devices that will incorporate the upcoming IEEE Wi-Fi 802.11ad protocol.


  • KEYWORD

    RF MEMS , Equivalent circuit modelling , Eigenfrequency analysis , Capacitive switch , Millimeter wave frequencies

  • I. INTRODUCTION

    In the last decade, various efforts have been made for radio frequency (RF) microelectromechanical system (MEMS) switches that are applicable to devices with switching activities that operate in RF to millimeter wave frequencies. MEMSs that are especially for RF applications have captured the interest of researchers from academia and industry. The RF MEMS has various advantages like high isolation, low insertion loss, low or near-zero power consumption, and low intermodulation distortion over their semiconductor counterparts like the field-effect transistor and p-i-n diode switches [1-5]. MEMS switches suffer from some drawbacks like low switching speed (due to mechanical deflection), high electrostatic voltage requirements of around 20–60 V for reliable switching operation, low power handling capability, reliability issues like average lifetime, fracture concerns, and packaging constraints [6-8]. RF MEMS switches incorporate a thin movable metal membrane, which actuates electrostatically for switching operations [9]. The lifetime of MEMS switches is one of the primary concerns for their use in repair-free applications like in remote places. After a few million switching cycles the metal membrane starts to suffer from fractures and this breakage usually occurs at high stress areas of the thin metal membrane.

    In this paper, we present the circuit characterization and eigenfrequency analysis of a wideband robust capacitive RF MEMS switch design that incorporates a thinlayered membrane of Poly-Si and Au millimeter wave frequencies. The switch design we present is simulated using commercially available EM solvers. We present the mechanical modelling viz. stress analysis that is reported in detail in [10], and the analysis using different proportions of materials is also reported in [10]. We numerically calculate the force distribution and equivalent circuit parameters of the RF MEMS switch. The basic model is taken as reference [9], and various components like the R, L, C, 𝚀-factor, and S-parameters are computed using the data of a Y-matrix, over a frequency sweep of 20–100 GHz. The first six eigenfrequencies are analyzed, and the equivalent modes are presented. The extracted and fitted RLC components of this switch over a range of frequencies divided into different frequency bands are also summarized in Section III. The proposed switch has huge potential for use in applications that operate on millimeter waves like satellite communication networks.

    II. DESIGN AND PRINCIPLE OF OPERATION

    The operational principle of the capacitive switch is mentioned in [11]. RF MEMS are usually actuated by the electrostatic principle [6]. For reliability and robustness of the switch, it is mandatory to design the switch with thick meanders to get an optimized range between the elastic recovery forces of metal and electrostatic voltage requirements for switching operation. The most common reliability issue in RF MEMS like stiction can be reduced, if the elastic recovery forces of the membrane are higher [12]. To overcome this issue of stiction, we have proposed a twin-layer membrane based on Gold (Au) and Polysilicon (Poly-Si). Gold has excellent electrical conductivity, but has low stress handling capabilities; in contrast, Poly- Si is a semiconductor, but has very high ultimate tensile strength to increase reliability. Gold (Au) is commonly used as a material for membrane design, but its ultimate tensile stress is 100 MPa, i.e., if the stress gradient crosses 100 MPa, the membrane can easily break from the areas under high stress. In contrast, the tensile strength of Poly- Si is 1.2 GPa [13] with a high Young’s modulus; thus using Poly-Si alone can increase the actuation voltage requirements.

    This switch incorporates a thin membrane of layered Au and Poly-Si. A layer of 0.2 μm thick Poly-Si is combined on top of a 0.5 μm thick Au layer. This combination provides high elastic recovery to reduce stiction and makes the switch more robust to handle many more switching cycles.

    The switch is designed on quartz substrate due to its better EM wave propagation capabilities on higher frequency bands [14]. A coplanar waveguide (CPW) with wide signal line of 60 μm and 40 μm gap between the ground plane is designed over the substrate to allow or block the RF signal using thin membrane. Input and output ports of the signal line are usually coupled with coaxial cables to connect with standard RF applications. Au material is used to design the CPW due to its better stiction with silicon nitride as dielectric over the substrate. Fig. 1 shows the proposed RF MEMS switch with labeled components. When the bias voltage is provided to the electrode beneath the signal line, electrostatic force is generated, which causes vertical deflection towards the signal line. A dielectric layer of 0.2 μm thick is used between the membrane and signal line contact to change the value of the capacitance.

    The capacitance varies either to allow the RF signal or to pass it through ground, i.e., block the RF signal. A large electrode of 80 μm × 60 μm is used for the actuation principle. The meanders help in reducing the pulldown voltage. Au is used to achieve low-voltage and Poly-Si is used for increasing robustness of the switch; hence, the best of both materials makes this switch reliable in high frequency applications. Fig. 2 demonstrates a close-up view of the membrane that shows twin layers stacked on each other. Holes are provided in the area of membrane that usually interacts with the signal line for the switching operation. Inclusion of holes in the membrane has huge advantages—it aids in attaining higher switching speeds, reduction of biaxial residual stress, reduction in air damping, and the effective mass of the membrane decreases [9]. The dimensions of the membrane are shown in Fig. 3 and the equivalent circuit model of the switch is shown in Fig. 4. The R, L, and C components are in shunt configuration of transmission as the switch is a shunt capacitive RF MEMS switch. The capacitance is a variable component in the shunt line. This variable component changes its value during switching. The specifications of the designed switch are given in Table 1.

    III. CIRCUIT CHARACTERIZATION

    The basic elements R, L, and C are extracted using commercially available EM-solvers [15]. The extracted values of these components are given in Table 2 for different frequency bands from 20–100 GHz. As the switch is a capacitive switch, the capacitance for ON-state or upstate and OFF or down-state is extracted. The corresponding fitted values are also given in Table 2. The table is summarized for the extracted and fitted value of R, L, and C for 60 GHz, V-band and for different frequency ranges. The switch performance is excellent around 60 GHz. The exact fit is computed according to the E-standards. The extracted capacitance in both states of switch for complete frequency sweep is shown in Fig. 5, and Fig. 6 indicates the series resistance and inductance. The 𝚀-factor for ON and OFF states is also computed and is shown in Fig. 7.

    For the capacitive RF MEMS switch in shunt configuration between signal line and ground, the impedance Zs is given by:

    image

    The impedance Zs can also be approximated from the Y-matrix data as:

    image

    The value of the capacitance depends purely on the position of the metal membrane suspended over the signal line. The capacitance depends on the ON or OFF state of the switch. The up-state capacitance Cup for the switch in ON state and the down-state capacitance Cdown for the switch in OFF state can be computed by plugging the values into Eqs. (3) and (4):

    image
    image

    where, ε0 is the permittivity of free space, w and W are the length and width of the actuation electrode, respectively, g0 is the gap between the switch membrane and signal line, td is the thickness of the dielectric layer, and εr is the permittivity of the material. The up-state capacitance Cup is 27 fF and the down-state capacitance Cdown is 1.4 pF.

    The primary factors for the calculation of the series resistance Rs are due to the transmission line loss, and also due to the membrane of the switch. The series resistance Rs is given as:

    image

    where, l is the length of beam, and Z0 is the characteristic impedance of the transmission line.

    Rs = Re (Zs) can also be used to estimate the series resistance Rs from the Y-matrix.

    The inductance L can be approximated from the Y-matrix data. The value of the impedance Zs is required from Eq. (2) to compute the inductance L as:

    image

    A high 𝚀-factor is desirable for any electronic switches, components or devices. Generally, a 𝚀-factor of above 15 is considered good for a variety of RF MEMS switches [9]. This proposed switch has excellent 𝚀-factors of above 27 in the ON state and above 15 in the OFF state as shown in Fig. 7. The 𝚀-factor can be computed for the ON and OFF states of the switch as:

    image

    where, Im (Y11) and Re (Y11) are the imaginary and real part of the two-port network, respectively, as shown in Fig. 4.

    The actuation voltage Vp required to actuate the switching mechanism can be computed using:

    image

    where, k is the spring constant and can be determined using Eq. (10), w is the length of electrode, W is the width of electrode, and g0 is the gap between signal line and membrane. The calculated Vp for this switch is 13.2 V.

    IV. EIGENFREQUENCY ANALYSIS

    Eigenfrequency basically means the ‘characteristic’ frequency of a device or in simple words, it is the ‘ownfrequency’ of the device. It can also be thought of as the normal modes of vibrations of a system. Eigenfrequency analysis was used to find the basic modes of vibration of the RF MEMS switch [14]. The first six modes of the switch are shown in Fig. 8. These frequencies can be determined by solving the Lagrangian of the system, and then applying the canonical equation. The deflection at the natural frequency of the RF MEMS switch or the first mode can be determined from Fig. 8. The series of next frequencies are at values that are whole number multiples of the fundamental frequency. The first six eigenfrequencies are given in Table 3.

    The equation of motion of a membrane that is subjected to harmonic force is considered. The harmonic motion of the mass-spring system in a single degree of freedom is usually modelled with a differential equation of second-order as:

    image

    where, meff is the effective mass of the membrane, γeff is the effective damping coefficient of the dielectric material, keff is the effective spring constant, and Fe is the electrostatic force. meff is composed of Au effective mass meff1 = 60.47 ng and Poly-Si effective mass meff2 = 4.63 ng, respectively, for the designed membrane. Hence, the total meff is meff1 + meff2 that leads to meff = 65.1 ng. The effective spring constant keff is composed of k' and k''. According to [9], the biaxial residual stress component k'' can be neglected due to the serpentine design, holes to release the biaxial residual stress, and the use of Poly-Si (as the stiffness of Poly-Si quite high). γeff can be determined by computing Eq. (9) by plugging all remaining values.

    As the membrane is composed of two materials, the spring constant k' is further composed of two components: ka for the Au material and kp for the Poly-Si. The spring constant can be computed using:

    image

    where, n is the number of meanders in the serpentine configuration, G = E/2(1 + v) is the torsion modulus, Ix = wt3/12 is the moment of inertia and the torsion constant is usually given by:

    image

    The effective spring constant keff for both components, i.e., ka + kp, can be determined by plugging material values like the Young’s modulus E and moment of inertia Ix into Eq. (10). The combined spring constant keff for the membrane is 5.1 N/m.

    The natural frequency of the membrane depends on the equivalent spring constant and the effective mass, and the natural frequency f0 is given as:

    image

    To determine the first mode of eigenfrequency f1, the component needs to be computed first for Au and then for Poly-Si. Then, the addition of these two factors can give the best estimate of the desired frequency. The first mode of frequency f1 can be determined by:

    image

    where, ρ is the mass density (mass/length) and L is the length of membrane.

    V. RF PERFORMANCE ANALYSIS

    The RF performances for the device in both switching states are extracted by S-parameters. The data of the S-matrix is computed for the 20–100 GHz frequency range [16]. Usually isolation, return loss in OFF state, insertion loss, and return loss in ON state are all required to examine the performance of switch in the RF region. High isolation and low insertion loss are in high demand in some applications, and that is where RF MEMS switches come into the picture. The proposed design gives excellent RF performance, with low voltage requirements. The switch is optimized for wideband millimeter wave frequencies. The S-parameters S11, S21 in both switching states can be computed using the extracted Y- and Z-matrix data by plugging the values in the equations given below. To compute the parameters in ON state, Y11−x will be used, where x = 1 for ON state and x = 0 for OFF state.

    image

    where, S11−x is the return loss on ON or OFF state depending on the variable x, Yz = 1/Z0, Y11−x = jωCdown for x = 0, i.e., in OFF state and Y11−x = jωCup for x = 1, i.e., in ON state. Y21−x = −jωCdown for x = 0 and Y21−x = −jωCup for x = 1, i.e., in OFF and ON states, respectively. To estimate the isolation S21−0 and insertion loss S21−1, plug the values into:

    image

    Excellent isolation above 50 dB can be achieved in the V-band and above 40 dB from 45–85 GHz. At 60 GHz, the switch results in maximum isolation of 58 dB. The results indicate 0.07 to 0.15 dB insertion loss in the ON state from 40–85 GHz. The return loss is in between 0.15–0.30 dB in the OFF state and 25–40 dB for 85 GHz and 40 GHz, respectively. The proposed switch also indicates moderate performance until 100 GHz with 35 dB of isolation and 0.2 dB insertion loss. The S-parameters in OFF state can be determined from the plot shown in Fig. 9 and the S-parameters plot for the ON state is shown in Fig. 10.

    Table 4 summarises the simulated RF performance results for the switch at different frequency bands. The RF performance for 40.60 GHz, 60–100 GHz, V-band (60–75 GHz), 60 GHz, and 45–85 GHz is given in the table. The plots shown in Figs. 9 and 10 indicate the RF performance from 20–100 GHz. The typical values for RF MEMS switches that operate in millimeter wave frequencies usually result in isolation of approximately 20 dB and insertion loss having typical values of 0.3– 0.4 dB, because on moving towards the higher frequency spectrum, the performance start decreasing.

    VI. CONCLUSION

    A wideband robust capacitive RF MEMS switch is designed and characterized. The combined layer membrane shows excellent RF performance in millimeter wave frequencies up to 100 GHz, while requiring low actuation voltage. The switch incorporates a twin membrane approach to increase the reliability operation of the switch. The high 𝚀-factor makes this switch an excellent choice for high-frequency applications. Maximum performance can be achieved at 60 GHz; hence, the proposed switch can be used in upcoming IEEE Wi-Fi standard 802.11ad that will operate at 60 GHz with data transfer rate up to 7 Gbps, or in cross link communication networks between satellites in a constellation.

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  • [Fig. 1.] Switch geometry of the proposed radio frequency (RF) microelectromechanical system switch demonstrating membrane over coplanar waveguide (CPW) and Si3N4 dielectric layer.
    Switch geometry of the proposed radio frequency (RF) microelectromechanical system switch demonstrating membrane over coplanar waveguide (CPW) and Si3N4 dielectric layer.
  • [Fig. 2.] Close-up view of layered Poly-Si and Au membrane, the image showing the 0.2 μm Poly-Si layer on top of 0.5 μm thick gold layer. The image shown is a close-up view taken from the corner area of the central part of membrane.
    Close-up view of layered Poly-Si and Au membrane, the image showing the 0.2 μm Poly-Si layer on top of 0.5 μm thick gold layer. The image shown is a close-up view taken from the corner area of the central part of membrane.
  • [Fig. 3.] Dimensions of layered switch membrane; the complete membrane acquires area of 240 μm × 80 μm.
    Dimensions of layered switch membrane; the complete membrane acquires area of 240 μm × 80 μm.
  • [Fig. 4.] Equivalent CLR circuit model of proposed switch. The circuit is shown for the shunt configuration of switch. Z0 are the terminal impedances and component C is variable, the value of C is varied by the position of metal membrane over the signal line.
    Equivalent CLR circuit model of proposed switch. The circuit is shown for the shunt configuration of switch. Z0 are the terminal impedances and component C is variable, the value of C is varied by the position of metal membrane over the signal line.
  • [Table 1.] Switch specifications
    Switch specifications
  • [Table 2.] Extracted and fitted values
    Extracted and fitted values
  • [Fig. 5.] Capacitance in ON and OFF states of the switch that results in ? 27 fF capacitance in ON state and variable according to the input frequency.
    Capacitance in ON and OFF states of the switch that results in ? 27 fF capacitance in ON state and variable according to the input frequency.
  • [Fig. 6.] Simulation result of resistance (Ω) and inductance (pH) of the MEMS switch, the inductance is high from the 40?80 GHz frequency range, and resistance drops almost linearly as per the input frequency, but lies between 0.7?0.4 Ω.
    Simulation result of resistance (Ω) and inductance (pH) of the MEMS switch, the inductance is high from the 40?80 GHz frequency range, and resistance drops almost linearly as per the input frequency, but lies between 0.7?0.4 Ω.
  • [Fig. 7.] ?-Factor in ON and OFF state of switch results in a great ?-factor of ? 25 in ON state and varies between 5?22 in OFF state.
    ?-Factor in ON and OFF state of switch results in a great ?-factor of ? 25 in ON state and varies between 5?22 in OFF state.
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  • [Fig. 8.] First six eigenmodes of designed membrane.
    First six eigenmodes of designed membrane.
  • [Table 3.] Eigenfrequencies and membrane deflection
    Eigenfrequencies and membrane deflection
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  • [Fig. 9.] Simulation of isolation (dB) and return loss (dB) in OFF state of RF MEMS switch. The results demonstrate isolation of ? 57 dB at 60 GHz region and less return loss towards higher frequencies.
    Simulation of isolation (dB) and return loss (dB) in OFF state of RF MEMS switch. The results demonstrate isolation of ? 57 dB at 60 GHz region and less return loss towards higher frequencies.
  • [Fig. 10.] Simulation of insertion loss (dB) and return loss (dB) plot for the RF MEMS switch in ON state. Excellent insertion loss of ? 0.1 dB and return loss of ? 30?40 dB were observed for 50 GHz and above.
    Simulation of insertion loss (dB) and return loss (dB) plot for the RF MEMS switch in ON state. Excellent insertion loss of ? 0.1 dB and return loss of ? 30?40 dB were observed for 50 GHz and above.
  • [Table 4.] RF performance analysis
    RF performance analysis