INSTITUTE OF PHYSICS PUBLISHING

JOURNAL OF MICROMECHANICS AND MICROENGINEERING

doi:10.1088/0960-1317/16/3/016

J. Micromech. Microeng. 16 (2006) 601–611

Microelectromechanical tunable capacitors for reconfigurable RF architectures Th G S M Rijks1,4 , P G Steeneken1, J T M van Beek1, M J E Ulenaers1, A Jourdain2, H A C Tilmans2, J De Coster3 and R Puers3 1

Philips Research, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands Interuniversity Micro-Electronics Center (IMEC), Kapeldreef 75, B-3001 Leuven, Belgium 3 KU Leuven, Department ESAT-MICAS, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium 2

Received 24 November 2005, in final form 23 January 2006 Published 14 February 2006 Online at stacks.iop.org/JMM/16/601 Abstract This paper reports on metal-based MEMS tunable capacitors, fabricated in a thin-film process on high-ohmic silicon. Continuous and reversible tuning has been demonstrated with an average tuning ratio of 4.5. A quality factor between 100 and 300 has been obtained in a frequency range of 0.5 to 4 GHz. The combination of a high quality factor and large tuning range makes these tunable capacitors very suitable as building blocks in many radio-frequency (RF) applications. The tuning speed, temperature stability and RF power handling have been studied in terms of self-actuation. Finally, the need for a hermetic package as well as a packaging concept which can potentially provide this has been demonstrated. After packaging, the devices can be handled as standard silicon dies, making them fit very well with a system-in-package approach. (Some figures in this article are in colour only in the electronic version)

1. Introduction In radio-frequency (RF) transceivers for wireless mobile communication, accurate and high-quality passive circuits are of prime importance. For example, the power-added efficiency of the transmit circuitry in the RF front end, consisting of power amplifiers, impedance matching networks, harmonic filters and switches, is to a large extent determined by the performance of the passives (including the switches) that constitute most of these circuits. Besides a high efficiency resulting in a low power consumption, small size and low cost are important drivers in the market of RF modules for mobile communication terminals. A very promising route of integrating high-quality passives in a cost-effective manner is using passive integration in a system-in-package (SiP) approach [1, 2]. In this approach, 4

Presently at Philips Lighting, LCD Backlighting, Hurksestraat 2c, 5652 AJ Eindhoven, The Netherlands.

0960-1317/06/030601+11$30.00

the passives are integrated on a chip or in a substrate using dedicated technologies, which are then combined with the active ICs in a modular fashion. In this way, different technologies and processes can easily be mixed and matched leading to an optimum of performance, cost and size of the RF module. This approach is illustrated in figure 1, showing an example of an RF transmit module [3]. A multilayer laminate substrate provides interconnect and embedded inductors, and acts as a mechanical carrier for the active ICs, passive ICs and surface mount device (SMD) components. The passive dies, indicated in the black rectangles, containing high-quality inductor/capacitor circuits, are manufactured in the Philips PASSITM process and mounted by flip-chip assembly [4]. The next step to bring down module size and cost, and increase functionality, is to implement a reconfigurable front end in which adaptive components such as tunable/switchable capacitors and switches enable parts of the circuits to be used for more than one frequency. In addition, these adaptive networks can be used to actively optimize the power-added

© 2006 IOP Publishing Ltd Printed in the UK

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Figure 1. Dual-band RF transmit module as a system-in-package: the multilayer laminate substrate (10 × 8 mm2) with interconnect and embedded passives carries active ICs, passive ICs (indicated in black rectangles) and SMD components [3].

efficiency of the front end as a function of the transmit power and the antenna impedance. This paper focuses on tunable capacitors, which are important building blocks in many RF functions such as voltage-controlled oscillators, tunable filters and antennas, and adaptive impedance matching circuits [5–7]. Most of these applications require low losses and a wide tuning range. The most common figures-of-merit are the tuning ratio, defined as the ratio of the maximum and the minimum capacitance, and the quality factor Q, which is the ratio of the imaginary and the real part of the impedance. For a capacitor Q equals 1/(ωCR), in which ω is the angular frequency, C is the capacitance and R is the (equivalent) series resistance. Nowadays, semiconductor bipolar diode varactors are generally used, utilizing the voltage-dependent capacitance of a reverse-biased p-n junction. Although state-of-art diode varactors can provide a considerable capacitance tuning (tuning ratios exceeding 4), they usually suffer from a large series resistance and therefore the quality factor at 1 GHz and 2 pF is limited to 10–20 [8]. Gated MOS varactors are more promising for RF applications, especially when processed in a silicon-on-insulator technology. A tuning ratio of 6.8 and a quality factor of 150 at 1 GHz and 2 pF have been claimed, however, not under the same biasing conditions [9]. More realistically, a tuning ratio of 3.5 combined with a quality factor between 5 and 70 has been found feasible. A drawback of semiconductor varactors is their poor linearity. Considerably higher quality factors can be achieved with tunable capacitors in MEMS (microelectromechanical systems) technology, making them also suitable for application beyond 1 GHz. A MEMS tunable capacitor in its most simple appearance is an air capacitor with a fixed and a movable electrode. The capacitance is tuned by varying the air gap and/or the electrode overlap area using electrostatic actuation. Electrostatic actuation is preferred for its inherent speed, low power consumption, typically 1 nJ per switching cycle, and simple implementation. A drawback of this form of actuation is that it requires high voltages, i.e. typically 10–50 V. A 602

wide variety of MEMS tunable capacitors, manufactured by bulk and/or surface micro-machining, has been reported in literature [6, 8, 10–19]. For continuous capacitance tuning, typical tuning ratios range from 1.35 to 3, depending on the design and choice of materials. The highest tuning ratios have been reported by Tsang et al [11] (tuning ratio = 5.3), Xiao et al [12] (tuning ratio = 7), Borwick et al [13] (tuning ratio = 8.4) and Muldavin et al [14] (tuning ratio = 15). Tsang reports on relay-type tunable capacitors in a thin-film technology based on poly-silicon. Xiao and Borwick have realized tunable capacitors in a SOI-like approach using bulk micro-machining. All these silicon-based devices generally suffer from a low Q factor and most of them require a large actuation voltage (up to 75 V) and/or a large actuation area. Muldavin realized a very high tuning ratio using the zipping effect of a curled trilayer cantilever, but requiring a high actuation voltage. Significant capacitance tuning starts at 40 V, and at least 70 V is needed to explore the complete tuning range. Q values have not been reported. Promising results on tunable capacitors with piezoelectric actuators have been published by Park et al [19]. They report a tuning ratio of 3.1 using an actuation voltage of only 6 V. The Q factor is 210 at 1 GHz; however, for a capacitance of only 66 fF. An advantage of piezoelectric actuation is the absence of a pull-in effect, which limits the gap tuning in electrostatic actuators. However, a distinct disadvantage is the complex and nonstandard processing that involves high-temperature steps and flip-chip bonding. High Q factors can be achieved in metal-based MEMS tunable capacitors. In this paper we report on MEMS tunable capacitors fabricated in an existing thin-film technology for passive integration. It will be shown that reversible capacitance tuning with a large tuning ratio can be achieved together with a high quality factor, while requiring only a moderate actuation voltage. Because of the high quality factor and low power consumption, these MEMS tunable capacitors are very promising building blocks to be combined with high-quality inductors and capacitors in a system-in-package approach, offering a potential for building a novel generation of RF front ends for mobile communication, mobile TV and base stations.

2. Design and fabrication As a technological and functional platform for the development of RF MEMS, an industrialized low-cost process for passive integration is used: the Philips’ PASSITM process [1, 4]. This thin-film technology on high-ohmic silicon combines three metal layers and two dielectric layers in only five mask steps to form high-quality integrated inductors and capacitors. A process cross-section is shown in figure 2. For the realization of RF MEMS, the standard process is slightly modified and extended with surface micro-machining as a back-end process module. The resulting process is a very simple and cost-effective approach to manufacture RF MEMS capacitive switches and tunable capacitors [20]. Additionally, the process is fully compatible with the standard infrastructure of the semiconductor industry and offers a fast route to the industrialization of RF MEMS.

Microelectromechanical tunable capacitors for reconfigurable RF architectures aluminum alloy (INT) aluminum (INS)

mechanical suspension

silicon oxide

silicon nitride

aluminum (IN)

bump VRF (air gap d1)

high-ohmic silicon passivation

Vact (air gap d2)

Figure 4. Schematic cross-section of a dual-gap relay-type tunable capacitor. The actuation capacitors with a large air gap d2 are separated from the RF capacitor with a small air gap d1. Bumps at the edges of the structure prevent pull-in of the actuation capacitors.

Figure 2. A cross-sectional view of the PASSITM process. aluminum (INS)

aluminum alloy (INT)

aluminum (IN)

aluminum oxide air gap high-ohmic silicon

Figure 3. A cross-sectional view of a MEMS capacitor in PASSITM technology, using two of the available metal layers. The native aluminum oxide (black) covers all metal surfaces that are exposed to air.

A cross-section of a MEMS capacitor in PASSITM is shown in figure 3, using two of the available metal layers. The substrate is high-ohmic silicon (resistivity ρ > 5 k cm) in order to suppress RF losses in the substrate. The bottom electrode consists of 0.5 µm aluminum (IN). The top electrode, which is used as the moving layer, consists of an aluminum alloy of 5 µm thickness (INT). It has been demonstrated that adding small amounts of alloying elements to aluminum thin films enhances the hardness and lowers the creep substantially [21]. Both the silicon nitride and silicon oxide layers act as sacrificial layers to create an air gap of 1.4 µm between the top and bottom electrodes. The native aluminum oxide, covering the metal layers, is used as a dielectric and avoids shorting of the electrodes. These thin dielectric layers facilitate a high capacitance density when the top and bottom electrodes are in contact. In fact, an average capacitance density of 250 pF mm−2 has been measured in MEMS capacitors with aluminum oxide as a dielectric layer. The aluminum oxide provides electrical isolation between the electrodes without significantly limiting the capacitance density as this is found to be governed by the surface roughness on each of the contacting surfaces. A drawback of the conventional parallel-plate MEMS capacitors in figure 3, in which the electrostatic actuation and the RF signal are superimposed, is that the ratio for reversible capacitance tuning is theoretically limited to 1.5 due to the socalled pull-in effect [22]. Pull-in occurs if the actuation voltage is larger than the pull-in voltage, at which the displacement of the suspended electrode exceeds 1/3 of the initial air gap. The result is that the suspended top electrode collapses on the bottom electrode. In practice, the tuning ratio is limited to 1.3–1.4 as the suspended electrode is generally not a rigid plate.

aluminum (IN)

aluminum alloy (INT) aluminum oxide air gap high-ohmic silicon

Figure 5. A cross-sectional view of a dual-gap relay-type tunable capacitor in PASSITM technology. All three metal layers are used to realize two different air gaps. The native aluminum oxide on the metal surface is indicated in black.

The pull-in effect can be avoided in a dual-gap relay-type tunable capacitor, schematically shown in figure 4 [18]. In the cross-section it is shown that the bottom electrode is patterned, separating the actuation capacitors from the RF capacitor. The suspended electrode is common for the actuation and RF capacitors. The RF capacitor is characterized by a small air gap d1 whereas the actuation capacitors have a larger air gap d2. If d2 > 3d1 continuous tuning of the complete air gap d1 can be achieved: the small gap will be closed before pull-in occurs in the actuation capacitors. The tuning ratio is determined by the capacitance density in the up state (at 0 V) and the down state. As the suspended top electrode and its mechanical suspension are not expected to act as an ideally rigid plate and springs, special bumps are designed to avoid the risk of pull-in at the edges of the structure. Dual-gap relay-type tunable capacitors can be realized in the PASSITM technology by utilizing all three metal layers. A process cross-section of a dual-gap relay-type tunable capacitor, an implementation of the design in figure 4, is shown in figure 5. Now, the top electrode and moving layer consist of INT that is locally, through a via, combined with INS (0.5 µm of aluminum). After removal of the silicon nitride between INS and IN, the small air gap of d1 = 0.4 µm is created. By removing both sacrificial layers between INT and IN, the large air gap of d2 = 1.4 µm is created. The gap ratio is d1/d2 = 0.3, just small enough to avoid pull-in.

3. On-wafer measurements 3.1. Capacitance measurements Figure 6 shows an example of a dual-gap relay-type tunable capacitor. The suspended electrode is attached to the substrate at four anchor points, through a mechanical suspension that is designed to prevent deformation as a result of thermal mismatch between the metal layer and the silicon substrate 603

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suspended electrode touches the bottom electrode of the RF capacitor. C(Vact )/C(0) has been calculated by solving the equilibrium equation of the electrostatic force and the spring force for the displacement x(Vact ):

Anchor

INT

Actuation Aí

A

d2

d1

RF capacitor

INS

100 µm

IN

Anti-pull-in bump

Figure 6. Top view of a dual-gap relay-type tunable capacitor. The close-up shows cross-section AA
of the segmented top electrode of the RF capacitor.

12

d0.333 1/d2= 1/3

11 10

d0.298 1/d2= 0.3

9

Tuning Ratio C(Vact)/C(0)

C(Vact)/C(0) Tuning Ratio

12 11 10 9 8 7 6 5 4 3

d0.25 1/d2= 1/4

8 7

d0.167 1/d2= 1/6

6

d0.111 1/d2= 1/9

5 4 3 2 1 0 0.8

0.9

1

V/Vclose

2 1 0 0

0.2

0.4

0.6

0.8

1

V/Vclose

Figure 7. Calculated C(Vact )/C(0) for different gap ratios, as a function of the actuation voltage that has been normalized to the closing voltage. The inset shows a blow-up of the curves.

[23]. The separate actuation electrode is compactly arranged around the RF electrode in order to have an efficient transfer of the electrostatic force to the RF capacitor. The tunable capacitor has been designed as a shunt capacitor; the suspended electrode is connected to the coplanar ground surrounding the device. The native aluminum oxide provides electrical isolation between the RF electrodes. Although the thin native oxide layer has a low breakdown voltage (<10 V), this does not impose a limit on the actuation voltage as there is no dc voltage difference over the RF capacitor, and the anti-pull-in bumps prevent the actuation electrodes from touching. The holes in the suspended electrode facilitate fast etching of the sacrificial layers. It has been described in the previous section that the top electrode of the RF capacitor is formed by combining a 5 µm and a 0.5 µm metal layer. Different (tensile) stress levels in the layers result in a stress gradient over the total thickness causing warping of the electrode. This is undesired as it tends to reduce the capacitance density in the closed state. In order to avoid that one layer exerts a force on the other the INS layer has been divided into segments of typically 600 µm2 that are attached to the INT layer through small vias (see the closeup in figure 6). Figure 7 shows the calculated capacitance ratio C(Vact )/C(0) as a function of the normalized actuation voltage for a gap ratio d1/d2 ranging from 1/3 to 1/9. C(0) is the capacitance when Vact = 0 V. The actuation voltage has been normalized with respect to Vclose, i.e. the voltage at which the 604

2 ε0 A2 Vact (1) = kx (Vact ) , 2 (d2 − x (Vact ))2 where A2 is the area of the actuation capacitor, Vact is the actuation voltage and k is the effective spring constant, and inserting x(Vact ) into d1 C(Vact ) = . (2) C(0) d1 − x(Vact ) The tuning ratio is determined by the ratio of the maximum and minimum capacitance density. The minimum capacitance density, determined by the air gap at 0 V, is 20.8 pF mm−2. The maximum capacitance density is governed by surface roughness and electrode deformation and is about 250 pF mm−2. This value has been derived from capacitive switches with the native aluminum oxide as a dielectric layer. As a result, the maximum expected tuning ratio is 12. The curves in figure 7 show a very nonlinear capacitance tuning as a function of the actuation voltage, showing a small slope dC/dVact at low voltage and a large slope close to Vclose. This is due to the inverse proportionality of the capacitance ratio with the displacement as well as the voltage dependence of the displacement itself. At d1/d2 = 1/3, the closing voltage is equal to the pull-in voltage of the actuator and pull-in is just avoided. It can be shown that the slope of the x(Vact ) curve diverges at the pull-in voltage. Therefore, the C(Vact )/C(0) curve (solid black line) shows a very large slope near the closing voltage. For smaller gap ratios, the pull-in voltage becomes considerably larger than the closing voltage and the divergence in x(Vact ) becomes less important. This is evidenced by a reduced slope near the closing voltage and by the fact that there is only a small difference between the curves with d1/d2 = 1/6 (black squares) and d1/d2 = 1/9 (solid light-gray line). Tuning curves with a steep slope are less practical for applications as the capacitance tuning becomes less accurate, and a feedback control loop for driving the tunable capacitor tends to become unstable. Therefore, a small gap ratio is preferred. In addition, a small gap ratio prevents the tunable capacitor from entering the pull-in regime in the case of a small upward deformation of the suspended electrode. However, for the same tuning ratio a small gap ratio inevitably results through a larger d2 in a higher actuation voltage. A gap ratio of 0.3 is applied to the devices under investigation. The relative sensitivity of the capacitance to variations in the actuation voltage is given by C −1 dC/dVact . For application of tunable capacitors in impedance-matching networks, the relative sensitivity of the impedance Z −1 dZ/dVact is the relevant parameter to be taken into account. Using impedance Z = 1/jωC, Z −1 dZ/dVact equals −C −1 dC/dVact . For application in frequency-tuning circuits such as a tunable VCO tank, the relative sensitivity of the resonance frequency −1 fres dfres /dVact is important. In a resonant circuit with inductance L, the resonance frequency fres is given by −1 dfres /dVact then 1/2π(LC)−1/2 . The relative sensitivity fres −1 equals −(2C) dC/dVact , a factor of 2 smaller than the relative sensitivity of the capacitance.

Microelectromechanical tunable capacitors for reconfigurable RF architectures

Y scan

Height (µm)

Height ( µ m)

X scan 3 2 1 0 -1 -2 -3 -4 -5 -6 100

200

300 400 500 X coordinate ( µm)

600

700

3 2 1 0 -1 -2 -3 -4 -5 -6 100

200

300 400 500 600 Y coordinate ( µm)

700

5

1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

4 3 2

C(Vact)/C(0)

In an earlier study [24, 25], the devices suffered from considerable upward deformation of the suspended electrode. Although this yielded record breaking tuning ratios, up to 17, the capacitance versus voltage curves were strongly influenced by the deformation even showing onsets of pull-in. In addition, reproducibility was very poor. By using a design with a temperature-compensated mechanical suspension and an improved process control, we are able to produce flat tunable capacitors with well-defined air gaps. Figure 8 shows a height profile of the suspended electrode that has been measured using a Wyko NT 1000 optical profiler. This profiler uses white-light interferometry to measure the height distribution of the metal layers over the sample. The line scans along the two directions evidence that the suspended electrode is flat to within 100 nm. By comparing the membrane height and the height of the (fixed) metal around it, it has been found that the air gaps are typically within 100 nm of their designed values. Four-point impedance versus actuation voltage measurements have been carried out at 1 MHz using a HP4275A LCR meter. The measurement setup is placed inside a glove box that is flushed with dry nitrogen (relative humidity < 0.1%) in order to eliminate effects of moisture in the ambient. In figure 9, the measured capacitance and tuning ratio are shown as a function of the actuation voltage. As we are interested in the capacitance of the MEMS device itself, the substrate capacitance and the capacitance of the coplanar wave guide (CPW) have been de-embedded. The contribution of the substrate capacitance will be discussed in more detail in section 3.3. The designed value for C(0) is 0.23 pF. The closing voltage Vclose, defined by the voltage with the highest dC/dV and indicated by the dotted line, is 13 V. For voltages smaller than Vclose, the tuning curve is very similar to the calculated

Capacitance (pF)

Figure 8. Height profile of the suspended electrode measured with an optical profiler. The top graph shows the height distribution as an intensity plot and the bottom graphs show line scans in the X and Y direction (indicated by the lines).

1

Vclose 0 0

5

10

15

20

25

30

Vact (V)

Figure 9. Measured capacitance and C(Vact )/C(0) as a function of the actuation voltage. The dotted line indicates the closing voltage Vclose.

tuning curves in figure 7. At Vclose the suspended electrode first touches the bottom electrode. Upon further increase of the actuation voltage, a more intimate contact between the electrodes is accomplished, finally resulting in a saturation of the capacitance. Measurement of about 100 samples distributed over two different wafers yields an average capacitance change of 0.8 pF (standard deviation is 12%) between 0 and 30 V, resulting in an average tuning ratio of 4.5. This is considerably smaller than the predicted tuning ratio of 12 (see figure 7), which was based on a capacitance density of 250 pF mm−2 in the closed state. The maximum capacitance of 1.17 pF in figure 9 is achieved with an electrode area of 0.0164 mm2, resulting in an effective capacitance density of 71 pF mm−2. Due to the segmentation of the top electrode, 0.0079 mm2 of the total electrode area has a remaining air gap of (d2 − d1) = 1 µm in the closed state, corresponding to a contribution to the total capacitance of about 0.07 pF. The remaining capacitance of 1.1 pF originates from the area of 0.0085 mm2 where 605

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15.2 V

((a) a ) closing closing

Tuning ratio C(Vact)/C(0)

15

C (a.u.)

15.1 V 14.9 V

10

14.7 V

5

5

(30)

4

(20) (17) (16)

(15.2)

(14.9)

2 (13.5)

(14.7)

(14.3) (12)

0

100

200

300

400

0

100

20 2

300

400

Figure 11. C(Vact )/C(0) versus closing time. The triangles have been derived from the measurements; the numbers in brackets indicate the actuation voltage in volts. The line has been calculated using equations (4) and (6).

((b) b ) opening opening X 10

15 1.5

C (a.u.)

200

t ( (µs) tclose (s) s)

tt ((µs) ( s) s)

15.2 V 15.1 V

10 1 14.9 V

topen 0.55

14.7 V 14.3 V

00 00

20 20

40

60

t (µs) ( s) s)

Figure 10. Response of a tunable capacitor to a block-function voltage on the actuation capacitor for different actuation voltages. (a) and (b) show the closing and opening of the tunable capacitor, respectively. tclose and topen are indicated by the arrows.

the top and bottom electrodes are in contact, resulting in a capacitance density of 129 pF mm−2. This shows that there is a large difference in the capacitance density in the closed state between relay-type devices and directly actuated switches. Obviously, the efficiency of the electrostatic force transfer from the actuation capacitor to the RF capacitor is far from ideal. When applying an additional actuation voltage directly between the RF electrodes, the capacitance in the closed state has been found to increase considerably (see section 3.5). 3.2. Transient measurements Time-dependent RF transmission measurements have been carried out in order to assess the tuning speed of the tunable capacitors. An RF signal generator has been used to generate a probing signal of 450 MHz with a peak voltage of 200 mV. The transmitted signal has been detected by a diode power sensor which is connected to an oscilloscope. For sufficiently low frequency and small capacitance values, a change in the output voltage of the detector is proportional to the capacitance change of the MEMS device. A periodic actuation voltage is provided by an arbitrary wave generator together with an amplifier. The measurements have been carried out in a glove box in 1 atmosphere of dry nitrogen. Figure 10 shows the response of the tunable capacitor to a block-function voltage on the actuation electrodes, the amplitude of which has been varied between 14.3 and 15.2 V. In figure 10(a) the voltage has been applied at t = 0 µs, and the subsequent capacitance increase has been monitored. The closing voltage of this device is 15 V. The capacitance change and the time in which it takes place depend on the actuation voltage. The closing time is defined as the time that it takes for the capacitance to saturate. It has been shown 606

(15.1)

14.3 V

tclose 0

(15.6)

3

1

0

(18)

that the closing time increases rapidly when approaching the closing voltage and decreases again when the closing voltage is exceeded. This effect is more distinctly demonstrated in figure 11, showing C(Vact )/C(0) versus the closing time tclose for actuation voltages between 12 and 30 V. The dynamic response of the moving electrode in the first order is described by the one-dimensional equation of motion dx d2 x + kx = Fel , +b (3) dt 2 dt where m is the mass, b is the damping coefficient and Fel is the electrostatic force. When neglecting the inertial force and using the same expression for the electrostatic force as in equation (1), the velocity v(x) is given by 
2 1 ε0 A2 Vact v(x) = − kx b 2(d2 − x)2 
2 (d1 − x)3 ε0 A2 Vact = − kx . (4) bsf 2(d2 − x)2 m

As the air gap d1 is small compared to the lateral dimensions, the damping force has been assumed to be governed by squeeze film damping in the RF capacitor, b=

bsf , (d1 − x)3

(5)

with squeeze film damping constant bsf [26]. The closing time for a certain actuation voltage has been calculated using  xe 1 dx, (6) tclose = v(x) 0 where xe is the displacement in equilibrium that is found by solving equation (1). Starting with an initial velocity v(0), the velocity decreases with increasing displacement of the moving electrode until it is zero in the equilibrium position. Moreover, when the voltage approaches the closing voltage, dv/dx approaches zero. This effect is even more enhanced by squeeze film damping and it results in divergence of the closing time. For actuation voltages larger than the closing voltage, the electrostatic force is larger than the spring force, which is limited to k · d1 . Therefore, the closing time decreases again with increasing actuation voltage. The line in figure 11 has been calculated using equations (2), (4) and (6) with k = 290 N m−1, bsf = 10−23 N m2 s and a minimum air gap in the closed state of 25 nm. Although the calculated closing

Microelectromechanical tunable capacitors for reconfigurable RF architectures

time diverges around Vclose, it corroborates the trends of the measured data. It must be remarked that the curves in figure 10(a) measured with an actuation voltage of 14.9 V and higher show multiple transitions. This is believed to be due to touch down of the different parts of the movable electrode that does not occur at exactly the same time. Similarly, the opening of the tunable capacitor is studied when the voltage is set to 0 V (figure 10(b)). Although the capacitance saturates only very slowly to the equilibrium C(0), the opening time topen has been estimated from figure 10(b), and is about 40 µs. The measurements presented here only give an indication of the tuning speed. In practice, the actual tuning speed is determined by the way in which the tunable capacitor is operated. 3.3. Equivalent RF circuit model and RF measurements The on-wafer RF performance of the tunable capacitors has been evaluated through one-port scattering-parameter measurements between 0.1 and 6 GHz using a HP8753D vector network analyzer and a ground-signal-ground probe. A oneport calibration has been carried out, i.e. an open, short and 50  load calibration, using calibration standards from a Suss MicroTec calibration substrate. From the RF measurements, an equivalent circuit model has been derived describing the tunable capacitor and its parasitics. The equivalent circuit model, shown in figure 12, has been implemented in Agilent’s ADS software. The total capacitance comprises the capacitance of the MEMS capacitor CMEMS, a stray capacitance to the coplanar ground Cstray, a capacitance Cpack between the signal line and a metal ring which is part of the package (see section 4), and a contribution from a 200 µm long 50  CPW that is used as interconnect. The equivalent series inductance and resistive metal losses have

Lossy inductor CPW

Rmetal(f)

LESL

CMEMS Cstray Cpack

Rsub

Figure 12. An equivalent RF circuit model for a packaged one-port MEMS tunable capacitor in a shunt configuration.

been introduced as a lossy inductor LESL the series resistance Rmetal of which scales with the square root of the frequency f due to the skin effect. An additional loss mechanism originates from the silicon substrate. Although the substrate is high ohmic, a nonnegligible amount of RF energy is transmitted through the substrate especially when the impedance of the MEMS capacitor is high compared to the impedance of the parasitic path through the substrate. Particularly at low frequency and for small capacitance values of the MEMS device, additional resistive losses are introduced by this parasitic path. It has been implemented in the model by a parallel resistor Rsub. In principle, the RF energy is coupled capacitively into the substrate but the impedance of coupling capacitors of a few picofarads can be neglected for frequencies larger than 100 MHz and sufficiently high Rsub. At lower frequencies, they indeed contribute to the total capacitance. That is why the impedance measurements at 1 MHz have been corrected for the substrate capacitance (section 3.1). Figure 13 shows a comparison between the measured (symbols) and simulated (lines) magnitude and phase of the

(a )

(c )

(b )

(d )

Figure 13. Magnitude and phase of the reflection coefficient S11 of a one-port tunable capacitor between 0.1 and 6 GHz in the open (left) and closed state (right). The markers indicate the measured data and the lines are the simulated data using the equivalent model of figure 12.

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0 V (open)

(a )

30 V (closed)

(b ) 500

400

400

Simulation

300

300

Simulation (isolating substrate)

Measurement

Q

Q

500

200

200

100

100

0

0 0

1

2

3

4

5

6

0

1

2

3

4

5

6

Frequency (GHz)

Frequency (GHz)

Figure 14. The quality factor of a one-port tunable capacitor between 0.1 and 6 GHz in the open (a) and the closed state (b). The markers indicate the measured data and the lines are the simulated data with (thick line) and without (thin line) substrate losses, using the equivalent model of figure 12. Table 1. Model parameters of the equivalent model of figure 12 to fit the data of figure 13. Cpack has not been used as the device under investigation was not packaged. Value

CPW length/width/gap CMEMS (open) CMEMS (closed) Cstray Cpack LESL Rmetal (f ) Rsub

200/100/67.5 µm 0.209 pF 0.79 pF 0.090 pF 0.05 pF 0.19 nH 0.15 · (f/1GHz)1/2  66 k

(a ) 1

Normalized ∆CC

Parameter

1.02

0.98 0.96 0.94 0.92 0.9 20

30

40

50

60

70

80

90

Temperature (oC) 1.05

608

(b ) Normalized V close close

reflection coefficient S11 of a one-port tunable capacitor. The large impedance mismatch between the 50  network analyzer and the MEMS device in the 0 V (open) state makes it hard to perform accurate one-port measurements, i.e. the measurements are very sensitive to calibration errors. For some frequencies the measurements even yield unphysical values for the magnitude of S11 (figure 13(a)). In that case only the phase information has been used for fitting the model parameters. Cstray has been determined separately from a scattering parameter measurement on a device with the membrane manually removed. Cpack can be calculated from the layout dimensions and is typically 0.05 pF. However, this parameter has not been used here as the device under investigation was not packaged. CMEMS, LESL, Rmetal and Rsub are determined from fitting the magnitude and phase of the reflection coefficient as a function of frequency for both the open and the closed state. The latter three parameters are the same for both states. The values of the model parameters are listed in table 1. Figure 13 shows that there is generally good agreement between the measured and simulated data. Figure 14 shows the quality factor Q as a function of frequency, in the open and the closed state, derived by converting S11 to the impedance and calculating the ratio of the imaginary and the real parts. The symbols denote the results of the measurement and the lines denote the simulations. The limited measurement accuracy in the open state yields unphysical Q values above 2 GHz in figure 14(a). The thin line in figure 14 represents the simulated Q without substrate losses, showing the typical 1/f behavior of a capacitor predicting very high Q’s below 2 GHz. The thick line, a simulation including substrate losses, shows a considerable reduction of the quality factor especially at low frequency. This is supported by the measured data and

1 0.95 0.9 0.85 0.8 0.75 20

30

40

50

60

70

80

90

Temperature (oC)

Figure 15. Normalized capacitance change C = (Cclose (T ) − Copen (T ))/(Cclose (25 ◦ C) − Copen (25 ◦ C)) and normalized closing voltage Vclose(T)/Vclose(25 ◦ C) as a function of temperature.

underlines that the effect of the silicon substrate, even if it is high-ohmic silicon, cannot be neglected for these devices. The maximum Q is 250 at 3 GHz (open state) and 300 at 1.4 GHz (closed state). Although there is a factor of 4 difference between the open- and closed-state capacitance, there is only a small difference in the maximum quality factor; the effect of a larger device capacitance is compensated by reduced substrate losses. The frequency at which self-resonance occurs is calculated to be 17.6 and 10.5 GHz in the open and closed state, respectively. 3.4. Temperature dependence The temperature dependence of the tuning range and the closing voltage have been studied between 25 and 80 ◦ C. The results are shown in figure 15. The values have been normalized to the value at 25 ◦ C. A decrease in the capacitance change C = (Cclose(T) − Copen(T))/(Cclose(25 ◦ C) − Copen (25 ◦ C)) of 7% has been observed at 80 ◦ C (figure 15(a)).

Microelectromechanical tunable capacitors for reconfigurable RF architectures 6

(a ) 5

C(Vact)/C(0) Tuning ratio

Assuming that Cclose does not depend on the temperature, this can be explained by a reversible temperature-induced deformation of the movable electrode that is not compensated for by the mechanical suspension, resulting in a decrease of d1 and therefore an increase of the open-state capacitance. A more substantial decrease with increasing temperature is noted for the closing voltage (figure 15(b)). A 7% decrease of d1 corresponds in the first order to a 2% decrease of d2, as d1/d2 = 0.3. As Vclose is close to the pull-in voltage it is expected to scale with d23/2, and a decrease of about 3% can be explained. Another mechanism for decreasing Vclose is a reduction of tensile stress in the moving electrode upon heating as the thermal expansion coefficient of aluminum is larger than that of the silicon substrate.

VDC,eq

3

0V 1V 2V 3V 4V 5V

2 1 0 0

5

10

15

20

25

1 Type 1 Type 1 Type 1 Type 2 Type 2 V-2/3 1/V(2/3)

(b )

(7)

where VRF is the peak voltage of the RF signal. The electrostatic force on the suspended RF electrode with area A1 is  1 ε0 A1 2 1 ε0 A1  2 Voc = − Fe = − 2VRF (1 − cos(2ωt)) . (8) 2 2 2 d1 2 d1 As the RF signal frequency is much higher than the mechanical resonance frequency, the tunable capacitor cannot respond to the cos(2ωt) component, but it will experience the dc component Vdc,eq = 2−1/2 VRF . Capacitance versus voltage measurements have been carried out with an actuation voltage on the actuation electrode and an additional dc voltage on the RF capacitor, mimicking Vdc,eq. Two types of devices, designed as in figure 6, have been studied: type-1 devices have an estimated spring constant of 120 N m−1 and type-2 devices have been designed with wider and shorter springs resulting in a considerably larger spring constant, k = 290 N m−1. The tuning curves of a type-2 device, measured with Vdc,eq between 0 and 5 V, are displayed in figure 16(a). It is illustrated that the closing voltage shifts to a lower value due to the extra electrostatic force component Vdc,eq. Additionally, pull-in occurs, therewith limiting the range for continuous and reversible capacitance tuning. The pi pull-in voltage Vdc,eq is derived from the general expression for the pull-in voltage [22] using (d1 − x(Vact )) as the air gap and A1 as the electrode area:  8k(d1 − x(Vact ))3 pi . (9) Vdc,eq (Vact ) = 27ε0 A1 It is dependent on the actuation voltage; when (d1−x(Vact )) decreases to zero with increasing actuation voltage, the tunable capacitor becomes more and more sensitive to pull-in. When

Relative tuning ratio

The RF power that is handled by the RF MEMS device can have a strong effect on its reliability, for example, through self-heating, but it can also prohibit normal operation of the device through self-actuation. The self-actuation effect has been studied here in more detail. The effect of the RF voltage on the performance of the tunable capacitor depends on the electrical configuration [22]. In the case of the one-port configuration described earlier, the open-circuit voltage, which is the voltage over the tunable capacitor in the open state (S11 ∼ = 1), is

30

Vact (V)

3.5. Power handling

Voc = 2VRF sin(ωt),

4

0.8

0.6

0.4

0.2

0 0

1

2

3

4

5

VDC,eq (V)

Figure 16. (a) C(Vact )/C(0) versus actuation voltage of a type-2 device with Vdc,eq ranging from 0 to 5 V. (b) Tuning ratio, normalized to the tuning ratio at Vdc,eq = 0 V, as a function of the Vdc,eq. Five tunable capacitors have been measured, three of type 1 and two of type 2. The dotted line indicates a V−2/3 dependence of the tuning ratio. pi

Vdc,eq becomes larger than Vdc,eq , pull-in occurs. It is observed in figure 16(a) that the capacitance in the closed state increases with increasing Vdc,eq, indicating that direct actuation of the RF capacitor results in a more intimate contact of the electrodes. Subsequent measurement of the tuning curve, after Vdc,eq had been set to zero again, showed that part of this capacitance increase has a permanent character: the tuning ratio increased from 3.3 to 4.3. For Vdc,eq > 3 V the tunable capacitor remains closed, even if Vact is set to zero. Figure 16(b) shows the tuning ratio for reversible capacitance tuning as a function of Vdc,eq, normalized to the tuning ratio at Vdc,eq = 0 V. This is in fact the reversible fraction of the tuning curve. The different symbols indicate different devices. At Vdc,eq = 0 V, the tuning curve is fully reversible (fraction = 1). It is shown that the reversible fraction decreases rapidly with increasing Vdc,eq. At Vdc,eq = 2 V, only 20% of the full tuning ratio remains. In fact, the tuning ratio approaches 1.3–1.5, the practical limit of a single-gap tunable capacitor. Similar results have been reported in [28]. As the tuning ratio scales with the gap (d1−x(Vact ))−1 (equation (2)) and the pullin voltage is given by equation (9), the reversible fraction is −2

3 expected to scale with Vdc,eq . The dotted line in figure 16(b) shows that there is indeed such a dependence. About 80% of the tuning ratio is preserved when Vdc,eq < 0.5 V. In a 50  system, this corresponds to a maximum RF power of 1.25 mW. Although the larger spring constant of the type-2 devices should make them less sensitive to self-actuation, these devices show only very little gain in the reversible fraction.

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(a )

Silicon/glass

(a )

pump out fill in

0.95 mm

High-ohmic silicon

0.95 mm (b )

Silicon/glass

Solder Sealed cavity

(b )

1.25 mm

High-ohmic silicon

Figure 17. Illustration of the IRS technique for hermetic MEMS packaging. (a) A cap with a solder ring is aligned and pre-bonded to the device wafer. Through an indent in the solder ring, the cavity is evacuated and subsequently filled with any gas. (b) Through reflowing the solder, the cavity is sealed hermetically.

MEMS tunable capacitors require zero-level encapsulation to protect their fragile moving parts during wafer separation, assembly and final use. As also moisture is considered to be detrimental for the device performance, hermetic sealing of the device cavity is preferred. A method for fabrication of hermetically sealed cavities has been described in [29, 30]. Using the so-called indent reflow sealing (IRS) technique, illustrated in figure 17, a glass or silicon cap is placed on top of the MEMS device using a reflow soldering process at 250 ◦ C. A metal ring is laid out around the MEMS device. A similar ring is processed on the cap with a solder layer on top (figure 17(a)). Next, the cap is aligned and pre-bonded to the device wafer. An indent in the solder ring makes it possible to evacuate the cavity and, if desired, fill it with any gas, e.g. dry nitrogen, prior to reflowing the solder. After reflow, the cavity that contains the MEMS device is sealed hermetically (figure 17(b)). Figure 18 shows discrete samples of an unpackaged and a packaged tunable capacitor. Figure 18(a) shows a 50 µm wide Cu/Ni/Au ring around the tunable capacitor for the solder ring. In figure 18(b), a high-ohmic silicon cap with a thickness of 100 µm has been soldered on top of this ring. The cavity is filled with dry air. The switch is connected to the outside world through underpasses underneath the metal ring, using the bottom metal. The contact pads around the device are meant for one-level interconnect to the RF board using bond wires. With a slightly different design of the contact pads, flip-chip assembly is possible [30]. The individual devices have been separated through laser dicing. Devices that have undergone the full capping and dicing procedure have been found to be still fully functional. This is evidenced by the tuning curve in figure 19 (squares). Only very small changes in capacitance and capacitance tuning have 610

Figure 18. (a) An unpackaged and (b) a packaged tunable capacitor. 4

3

C(Vact)/C(0)

4. Packaging

1.4 mm

2 Capped/diced 1

After storage After drying

0 0

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Vact (V)

Figure 19. C(Vact )/C(0) as a function of actuation voltage directly after capping and dicing (squares), storage in ambient atmosphere (triangles) and heating to 75 ◦ C and cooling down again (crosses).

been found before and after capping. In order to study the hermeticity of the package, the samples have been stored in ambient atmosphere for several weeks after which the tuning curve has been measured again. The triangles in figure 19 represent the tuning curve after storage. It shifts toward smaller actuation voltages, shows non-reversible tuning, and pull-in is clearly observed. It is believed that this is caused by moisture-related charging of the RF capacitor. After ‘drying’ the capacitor by heating it to 75 ◦ C in a dry nitrogen flow and subsequently cooling it to room temperature again, the initial reversible tuning curve has been restored (crosses in figure 19). This experiment shows that the package is not hermetic, corroborates the idea of moisture-related charging and underlines the necessity for a hermetic encapsulation. There are two possible explanations for the failing hermiticity: (i) the amount of solder used was not sufficient and (ii) the

Microelectromechanical tunable capacitors for reconfigurable RF architectures

width of the solder ring is too small. At the position where the signal line crosses the solder ring, its width is only 20 µm in order to reduce the parasitic capacitance of the package. Further experiments are ongoing.

5. Conclusions Metal-based MEMS tunable capacitors have been fabricated in a thin-film process on high-ohmic silicon. Continuous and reversible tuning has been demonstrated with an average tuning ratio of 4.5. A quality factor between 100 and 300 has been obtained in a frequency range of 0.5 to 4 GHz. The combination of a high quality factor and a large tuning range makes these tunable capacitors very suitable as building blocks in many RF applications. The tuning speed has been found to be strongly dependent on the actuation voltage. Although the mechanical design has been optimized for temperature stability, a small temperature dependence of the capacitance and the closing voltage has been observed between 25 and 80 ◦ C. In addition, it has been established that this type of tunable capacitor can only be used at low RF power levels, as the small air gap of the RF capacitor makes it sensitive to self-actuation by the RF voltage. Finally, the need for a hermetic package as well as a packaging concept, which can potentially provide this, has been demonstrated. After packaging the devices can be handled as standard silicon dies, making them fit very well with a system-in-package approach.

Acknowledgments This work has been carried out as part of the IST project MEMS2TUNE under number IST-2000-28231. The authors would like to thank M den Dekker for laser dicing.

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