Tunable Micro-Electromechanical Systems

Abstract

  A tunable micro-electromechanical systems integrated inductor with a large-displacement electro-thermal actuator is discussed here. Based on a transformer configuration, the inductance of a spiral inductor is tuned by controlling the relative position of a magnetically coupled short-circuited loop. Theoretical studies are backed by a variety of fabricated and measured tunable inductors that show a 2 : 1 inductance tuning ratio over a wide frequency range of approximately 25 GHz. In addition, the maximum and minimum quality factors of the tunable inductor are measured to be 26 and 10 which is high compared to previous designs. They can considerably extend the tuning capabilities of critical reconfigurable circuits such as tunable impedance matching circuits, phase shifters voltage controlled oscillators, and low noise amplifiers.

Introduction  

                  MEMS are miniaturized device / array of devices combining mechanical and electrical components fabricated using IC batch production techniques. RF MEMS components are used for RF & MW and millimeter wave circuits. They are small devices of feature size of micron order.  Fabricated by nano and micro technology. RF micro-electromechanical systems (MEMS) have been a rapidly growing field within the MEMS industry. In particular, a wide range of RF MEMS switches, varactors, and high- inductors have been developed and demonstrated over the last two decades. However, few solutions have been presented for obtaining tunable (or variable) MEMS inductors.   

                 The approaches reported in the literature today for realizing a tunable MEMS inductor include: 1) control of the magnetic-core-material properties by changing the core permeability or displacing the core material; 2) usage of MEMS switches to digitally control the winding; 3) control of the mutual inductance between the turns of the inductor itself; and 4) control of the mutual inductance between the primary inductor and a separate short-circuited inductor. 

                   Each of the demonstrated techniques has serious shortcomings that have not allowed RF designers to utilized tunable inductors in their designs. Changing the core permeability and consumes has resulted in very low quality factors significant amount of dc power (15-300 mW). In addition, movement of the core material requires large and complex actuators. Switchable inductors are limited by the number of switches utilized. Few switches result in a limited set of available values, while many switches drastically drop the quality of the inductor and result in large and narrowband circuits. Controlling the mutual inductance between the turns of the inductor itself has shown very limited inductance variations ( 18%). The fourth technique relies on coupling the inductor to be tuned (primary inductor) to a short-circuited inductor (secondary inductor) and controlling their coupling coefficient. In [4], both the primary and secondary inductors are implemented as single-turn loops. An electrostatic actuator changes the position of the short-circuited loop. This design exhibits a tuning ratio of 1.54:1 and requires very high electrostatic actuation voltages (150 V) and many complex fabrication steps. Besides this tuning ratio, no other information (e.g., quality factor and bandwidth) is given in [4]. The reported results show high inductance tuning ratios of 2:1 and good quality factors of 15-21 for the entire tuning range. However, these are not integrated solutions because they rely on manual movement for reaching the required displacements. In addition, no information is provided in any of these papers on how the inductance and resistance of the short-circuited inductor affect the critical RF parameters of the tunable inductor. Consequently improved designs and implementation methodologies are needed for achieving simple structures with high and continuous tuning ranges, high quality factors, large bandwidth, and low occupied chip area.

  Here, measured and theoretical results for an optimized tunable MEMS spiral inductor with an integrated large-displacement electro-thermal actuator are analyzed. The tunable MEMS inductor utilizes an integrated transformer configuration, which is composed of two magnetically coupled inductors. Tunability is achieved by varying the magnetic coupling coefficient (k) that is dominated by the distance between the two inductors. Results derived by a simple equivalent circuit, full-wave simulations, and measurements indicate that optimal RF performance requires minimized resistive losses on the secondary inductor.

Analysis and design of tunable inductor

   The operating principle of the presented tunable inductor can be explained on the basis of an integrated transformer configuration, as shown in Fig. 1. The primary coil is the coil whose inductance needs to be controlled. The secondary coil is short circuited and magnetically coupled to the primary one. The magnetic flux linkage between the coils induces eddy currents in the secondary coil. When the magnetic coupling between the inductors is changed, the equivalent inductance seen at the primary port is also changed. This is the main concept behind this tuning approach. However, existing studies have only considered the case where the two coils are identical. Here we analyze for the first time the generalized equivalent circuit of two different coils and investigate the associated design methodology to attain an optimal performance. In addition, we perform high-frequency full-wave simulations with Ansoft’s High Frequency Structure Simulator (HFSS) and mechanical simulations with ANSYS to predict the performance of the proposed tunable inductor structure.

These equations are more general than those above and can be used to optimize the design. Specifically, we can clearly see from these equations that increasing k decreases , but at the same time increases .

To obtain the largest possible inductance variation and highest quality factor over a wide frequency range, we investigate   as a function of k for different secondary inductances (L2) and resistances (R2). While the model in Fig. 1 is relatively simple, it provides significant physical insight, which as shown later, is verified by fullwave simulations and measurements. As can be deduced from (5), not only R1, but also the ratio of the   secondary inductor should be minimized for attaining a small   (correspondingly higher quality factor). In order to investigate the effect of   on   and bandwidth, we first perform HFSS simulations to obtain different possible   ratios for typical spiral inductors. Typical octagonal spiral inductors (in air) with different number of turns and metal thickness are simulated to obtain the necessary inductance and resistance values. As shown in Fig. 2, a higher number of turns and thicker metal traces lead to smaller  . We can also observe that this ratio is a weak function of the number of turns for thick metal traces.

We can make the following three important observations.  

1) The low end of the bandwidth of the tunable inductor is inversely proportional to the   ratio. This low end is approximately 1 GHz when  =1.3[Ω/nH] and becomes 10 GHz when  =17[Ω/nH].

2) The high-frequency tuning ratio as a function of k is identical for all cases and agrees well with (4). The high-frequency ratio will be limited by the parasitic capacitance of the primary coil, which has been ignored here. This is, however, taken into account later in this paper by full-wave simulations and  measurements.

3) While the high-frequency is   increased as a function of  k for all cases, this increase is rather modest (from 5 to 7.25 ) for smallest   =1.3[Ω/nH] and becomes prohibitively  high largest  =17[Ω/nH].

 Electrothermal Actuator

                   Electrothermal actuators are used for moving secondary  short circuit loop wrt primary because simple fabrication, low actuation volts, lack of pull in instability.

Electrothermal actuator working

• It  composed of two bimorph (Ti/SiO2)actuator arms   anchored on substrate.
• These arms support the short circuited secondary  inductor.
• Applied voltage between two anchors induces a current  flow on Ti layer resulting in Joules heating and bimorph  bends down. It is because of fact that Ti has greater value for the coefficient of thermal expansion than SiO2. So Ti elongates more than SiO2 bending the structure downward.

  In this tunable inductor, we control the magnetic coupling between the two coils by controlling their relative distance and overlap area. In this technique, a large displacement (>100um) is critical in achieving a significant variation in the magnetic coupling coefficient  that leads to a large inductance tuning range. To accomplish a large vertical displacement by MEMS actuation, we adopt an electrothermal actuator due to its simple fabrication process, low actuation voltage, and lack of pull-in instability. As shown in Fig. 5, the electrothermal actuator is composed of two biomorph Ti/Si O actuator arms anchored on the substrate. These arms support a thick electroplated gold loop that constitutes the short-circuited secondary inductor. The high thickness for this loop is needed for two reasons, which: 1) results in the lowest possible resistance for the secondary coil and 2) results in a very planar secondary coil despite the fabrication residual  stress.

   The analysis of this actuator was performed by ANSYS with the material properties listed in Table I. An applied dc voltage between the two anchors induces a current flow on the Ti layer resulting in Joule heating that causes the biomorph beams to bend downwards. This is shown in Fig. 5. Fig. 6 depicts the tip deflection in terms of input power. When 0.13 V is applied at the  anchors, the nominal dc resistance and current on the actuator  wa =20um and   La =200um are 3.7 and 35.1 mA, respectively. Therefore, the tip deflects by 144 m (34% of the  total length ) with an input power of 4.6 mW.

Electromagnetic Simulation

   We considered two different possibilities for the primary 2-D spiral tunable inductor. In the first case (type 1), the primary spiral is printed on the substrate [see Fig. 7(a)], while in the second case (type 2), it is suspended in air anchored on the substrate by two via holes [see Fig. 7(b)]. Type 2 may appear more attractive because of its significantly lower parasitic capacitance to the substrate that results in higher quality factor and self-resonant frequency. On the other hand, it imposes strict requirements on the fabrication process since a very low residual stress is needed to maintain a planar profile that will prevent a direct contact with the suspended secondary inductor. The final choice depends on the maturity of the employed fabrication technology. 

   The electrothermal actuator presented in Section B moves the short-circuited secondary loop along a curvilinear path. We employed HFSS to model the tuning behavior due to this movement. The simulated inductance and quality factor as a function of the tip height of the short-circuited loop are depicted in Fig. 8. As expected, when the tip height is decreased, the frequency-dependant inductance and quality factor are also decreased. It is also worth noticing the differences between Figs 8(a) and (b). Fig. 8(a) depicts the results of a 4- m-thick Au spiral coupled to a 4- m-thick Au short-circuited loop, while Fig. 8(b) shows the results of the same spiral when coupled to a 0.5- m-thick Ti short-circuited loop (both loops have a 0.5- m-thick SiO layer underneath their metal layer). The latter figure clearly shows the limited inductance variation at lower frequencies and the rapid degradation of the quality factor as the short-circuited loop deflects downwards. In Section , we demonstrated that the resistance of the loop has a considerable effect on the equivalent resistance and bandwidth of the variable inductance. Thus, these results from HFSS confirm the results of the simple equivalent-circuit model of Fig. 1. The magnetic coupling coefficient k is also extracted from Fig. 8 using (4). As can be seen in Fig. 9,  k decreases sharply as the short-circuited loop approaches the spiral, but saturates for large tip heights. Therefore, in an optimal design, the initial deflection caused by the residual stress should be carefully controlled to minimize the actuation power required to move the short-circuited loop close to the spiral. 

Fabrication steps

   The fabrication process requires six masks and the required steps are summarized in Fig. 10. These steps produce a spiral printed on the substrate. If a suspended spiral is desired, we can switch the order of the spiral and metal bridge steps. The coplanar waveguide line and spiral are made of a gold-electroplated thick metal (2 or 4um) first [see Fig. 10(b)]. After removing the seed metals Ti/Au (50/100 nm) and the photoresist electroplating mold (AZ9260), the first sacrificial layer (S1827) is deposited and the actuator anchor points and the metal bridge vias are photo lithographically defined [see Fig. 10(c)]. Afterwards, the metal bridge (1 m of Au) is deposited and defined through a wet-etch process [see Fig. 10(d)]. The second sacrificial layer (S1827) is subsequently spun to separate the spiral inductor from the short-circuited loop [see Fig. 10(e)]. In the next step, the actuator and the seed metal layers (SiO Ti Au of 500/500/100 nm) are simultaneously deposited [see Fig. 10(f)]. The seed metal layer (100 nm of Au) is intended for the gold electroplating of the short-circuited loop (4um). The last step is the removal of the sacrificial layer and the supercritical CO2 drying (CPD) of the structure [see Fig. 10(g)].

Experimental results

Fabricated the inductor with various design parameters including the number of turns, spiral metal-trace width, spiral diameter, and actuator arm width and length. Fig. 11 shows typical scanning electron microscope (SEM) images of the inductors. The spirals are suspended in air (type 2) for reduced parasitic. As shown in Fig. 11, the electrothermal actuator is curled upwards after release due to the internal residual stress. Excessive residual stress in the metal layers, however, can significantly distort the spiral, as shown in Fig. 11(b). Additionally, excessive residual stress also leads to a suboptimal actuator performance that consumes higher dc power (at least tens of mill watts). 

The measured equivalent inductance and quality factor variation as a function of dc input power over a bandwidth of 30 GHz. The fluctuation in the quality factor data are due to its very sensitivity to measurement errors, especially at very high frequencies. In addition, measured results of different tunable inductors are compared. 

The following can be deduced from these measurements. 

1) A nearly constant inductance variation ratio is obtained over a very wide frequency range of approximately 25 GHz. As previously explained, this is due to the very low resistance obtained from the wide and thick-electroplated short-circuited loop.

2) The measured inductance variation is approximately   2: 1.

3) Electrothermal actuators with narrower wa and/or longer La require lower actuation powers for a given deflection.

4) As the short-circuited loop approaches the spiral, the inductance and quality factor variation become saturated. This agrees well with the electromagnetic simulations.

            Based on experimental results the equivalent circuit is modified as fig 16. and simulation results with the modified equivalent circuit shows better  similarity with the experimental results.  Here additional factors like Cs (substrate capacitance), Rsub (substrate resistance), and Cox oxide layer capacitance are also considered.

Conclusion

 A novel tunable MEMS integrated inductor with an integrated large-displacement electro thermal actuator was discussed here. This tunable MEMS inductor is composed of two magnetically coupled inductors. The primary inductor is a 2-D integrated spiral, while the secondary inductor is a simple short-circuited loop. This paper also presented a detailed study that presents specific design guidelines for achieving optimal designs. The short-circuited loop is attached to the pre-deformed electro thermal actuator that deflects downwards when the appropriate bias power is applied. Here utilized finite-element electro-thermo-mechanical and electromagnetic models to design this inductor. In addition, we present compact physics-based lumped-element models that agree favorably with the measured data. The fabricated tunable inductor shows a measured 2: 1 inductance tuning ratio over 25 GHz with a maximum quality factor that varies between 10–26.