Capacitive RF MEMS analytical predictive reliability and lifetime characterization

Microelectronics Reliability 49 (2009) 1304–1308

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Capacitive RF MEMS analytical predictive reliability and lifetime characterization Mohamed Matmat a,*, Fabio Coccetti a, Antoine Marty a,b, Robert Plana a,b, Christophe Escriba a,b, Jean-Yves Fourniols a,b, Daniel Esteve a a b

CNRS; LAAS; 7 Avenue du colonel Roche, F-31077 Toulouse, France Université de Toulouse; UPS, INSA, INP, ISAE; LAAS; F-31077 Toulouse, France

a r t i c l e

i n f o

Article history: Received 26 June 2009 Available online 8 August 2009

a b s t r a c t The reliability of integrated systems is considered as a major obstacle in their development. The goal of this work is to estimate the lifetime of RF MEMS capacitive switch devices. This is performed by combining the functional and physical failure analysis models using the VHDL-AMS language. The physics of charging effects along with mechanical behavior of the membrane are introduced simultaneously to determine the time to failure. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction There are two existing ways to estimate the stable functionality and reliability of a micro-system. First, the statistical approach based on experimental measurements of many devices. This approach results in increased cost, required time and effort. The second is the prediction approach based on physical model of the device [1,2], a methodology which is still not mature and requires more effort at the level of multi-scales multi-physics modeling. This calls to establish a procedure for evaluating the reliability of a micro system. The objective of this work is to build a reliability model in order to be able to simulate a micro-system’s behavior as a function of time under several operating conditions [3,4]. This model is supposed to be able to address and give estimations for several MEMS device characteristics, mainly to evaluate and detect the instant of failure, i.e. the lifetime, which is defined as the time consumed by the MEMS device before a failure occurs and working at accepted performance levels. 2. Our approach The flowchart shown in Fig. 1 illustrates a general methodology for the evaluation of a micro-system reliability prediction, assuming normal working conditions under normal environment. This consists in:  Identification of the physical origins of the micro system failures.

* Corresponding author. Tel.: +33 (0)5 61 33 63 62; fax: +33 (0)5 61 33 69 08. E-mail address: [email protected] (M. Matmat). 0026-2714/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2009.06.049

 Modeling of these physical phenomena, based on the corresponding laws of physics.  Transformation of the physical models into a VHDL-AMS language [4,5], compatible with system simulations, i.e. create several system models associating functional representation and instability phenomena.  Predictive reliability evaluation by simulating the system functionality with the instability model, assuming real working and environmental conditions. All these steps constitute a virtual reliability prototype [3]. 3. RF MEMS physical failure development It is known that a micro-system based on silicon exhibits a temporal instability characterized by huge time constants. In the case of bipolar and MOS transistors, the involvement of thermal silicon oxide is the major contributor for good stability and reproducibility. These reliability issues have become important once again for the performance of RF MEMS. In RF MEMS [2], the dielectric is used as an isolation layer that is subjected to extreme electrical and mechanical transient conditions. The charging effect phenomenon is often characterized as a bias-shift of the switch’s Vpullin and Vpullout voltage (switch on, switch off voltage) [6]. This phenomenon is well known and has been identified in different kinds of dielectric layer. The basic model is probably related to local changes of electron positions around deep traps; taking into account the barrier involved in this change of electron position, the expected time constant can be very long: hours or days. We propose that effect can be globally represented as a change in dielectric constant of the layer. The source of this polarization is the time dependency of the dielectric constant of the material used in the RF-MEMS device.

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M. Matmat et al. / Microelectronics Reliability 49 (2009) 1304–1308

Fig. 1. The current approach for a reliability model.

Due to the application of the action field, i.e. voltage, the dielectric constant exhibits unstable behavior over time. The variation in this constant can be expressed as follows:

@ er ef  er ¼ @t s

ð1Þ

Ca

Vcmd

where



Ei s ¼ s0  exp kT

ð3Þ

is the dielectric permittivity in permanent regime. When a Heaviside function voltage is applied, the solution of Eq. (1) submitted to a level of tension Vf  Vi, becomes:

er ðtÞ ¼ ef þ ðei  ef Þ  exp

  t

s

ð4Þ

ei is the dielectric permittivity at t = 0. A t

e0  er  A

C v ðtÞ ¼

Cv

Vdrift

t

e0  er ðtÞ  A t

Fig. 2. The functional model: C a is the air capacitance which varies according to the effective air gap, C d is the dielectric capacitance, C v ðtÞ represents the slow polarization phenomena.

Ca  V1 Ca þ C0 Ca  V2 Q 2 ¼ C d  V d ¼ ðC 0 þ C v Þ  Ca þ C0 þ Cv Q 1 ¼ C 0  V c0 ¼ C 0 

ð5Þ

which represents the dielectric capacity variation over time. In an equivalent electrical model, the slow polarization phenomena in this dielectric material can be modeled by two parallel capacitances C 0 and C v , defined:

C0 ¼

C0

ð2Þ

ef ¼ a  V cmd

C v ðtÞ ¼ e0  er ðtÞ 

C0

Vcmd Cd



is the time constant of an activation energy Ei .

where

Ca

ð8Þ ð9Þ

At the time of switching (see Fig. 3), we have Q1 = Q2 resulting in what can be translated as an offset (Shift) on the bias command V2  V1. Solving the previous equation Q1 = Q2, we obtain the voltage shift V Shift :

V Shift ¼ V 2  V 1 ¼

C a  C v V1 ðC a þ C 0 Þ  ðC 0 þ C v Þ

ð10Þ

ð6Þ ð7Þ

where C0 is a constant capacitance counts for the dielectric material assuming that this capacitance is not affected by the charging effect.

Our proposal, as shown in Fig. 2, is to introduce, in the functional model of RF MEMS device, a drift voltage V Shift to counts for the charging in dielectric constant [1]. The calculations of this voltage amplitude are detailed in the next paragraph. Moreover, the activation of the RF-MEMS operates at a known value ‘‘Q‘‘ which fixes the electrostatic force; if C v changes with e, it will be necessary to vary V with DV value:

Ca

Ca

4. Physical to electrical model transcription

Q1 V1

Q2 V2

C0

Cd

C0

Fig. 3. Ideal case and case with charging effect.

Cv

M. Matmat et al. / Microelectronics Reliability 49 (2009) 1304–1308

5. Results To demonstrate our approach, we chose a ¼ 1 and s ¼ 50 s. The input signal for our VHDL-AMS model is a 50 s voltage step signal with an amplitude of 40 V as depicted in Fig. 4a. The prediction of C v ðtÞ is shown in Fig. 4b. The simulated drift voltage is presented in Fig. 4c [1,7]. These data ensure that the applied voltage signal parameters results in a saturated performance

30

20m

4p 3p

12m

15m

10m

5m 1p 0

20

40

60

0 100

80

10m 8m 6m 4m

2p

0

Unipolar signal Bipolar signal

14m

6p 5p

15

16m

7p

Capacitance (F)

Bias voltage (V)

25m

8p Bias voltage Cv Capacitance Vshift (V)

Vshift (V)

45

of the voltage drift, confirming that our modeling is in good agreement with material physics. The main issue is to optimize the control signal parameters in order to minimize the drift voltage [7,8]. The drift voltage has been recorded by changing the control signal amplitude [10], duty cycle and signal form, as shown in Figs. 5–7, respectively. As the amplitude increases, the drift voltage increases [9]. As the duty cycle increases, the drift voltage increases. It is observed that above the

Vshift(V)

1306

0

2m 0 10

100

1000

Time (s)

Time (s) Fig. 4. Dielectric capacitance variation and drift voltage controlled by bias voltage (a) versus time with a ¼ 1 and s ¼ 50 s.

22m

Fig. 7. Drift voltage versus time (logarithmic scale) for different applied voltage signal forms with a ¼ 1 and s ¼ 1000 s.

35 V 50 V 80 V

20m 18m

Vshift(V)

16m 14m 12m 10m 8m 6m 4m 2m 0 10

100

1000

Time (s) Fig. 5. Drift voltage versus time (logarithmic scale) for different applied voltage amplitudes with a ¼ 1 and s ¼ 1000 s.

20m

Duty cycle 20% Duty cycle 40% Duty cycle 60% Duty cycle 80%

18m 16m 14m

Vshift(V)

12m 10m 8m 6m 4m 2m 0 10

100

1000

Time (s) Fig. 6. Drift voltage versus time (logarithmic scale) for different duty cycles with a ¼ 1 and s ¼ 1000 s.

Fig. 8. (a) Capacitance voltage dependency (cycling) and (b) blow out of area in Fig. 8a.

M. Matmat et al. / Microelectronics Reliability 49 (2009) 1304–1308

threshold of 70%, the variation of drift voltage is small due to the reduction in the discharging time [8,10]. This is explained by the dielectric time relaxation needed to get rid of the charging effect. When a square bipolar signal form is applied, the drift voltage decreases, as one can conclude by comparing the two curves in Fig. 7. It can be seen that the slope of the voltage drift is strongly reduced by using the bipolar signal [7,11]. These results are in good agreement with physical behavior and reported data in the literature. The next task in our approach is to estimate the time to failure (TTF). Cycling has been conducted over time. A square unipolar voltage signal is applied with amplitude of 40 V. The capacitance voltage dependency has been recorded. The trace of this C–V curve is represented in Fig. 8. The most important information that can be extracted is the shift on Vpullin and Vpullout voltage. The Vpullout is the major parameter to be observed [2,12]. The shift on Vpullout increases until it approaches zero that indicates a sticking of the membrane with the dielectric material (TTF). Fig. 8b shows a blow out of Fig. 8a.

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Fig. 10. Schematic of the RF-MEMS reliability test bench.

6. Experimental 6.1. Device structure The device used in this study is an RF MEMS capacitive switch fabricated on a silicon substrate. It consists of a fixed–fixed thin metallic membrane suspended over a bottom electrode, insulated by a dielectric film, as illustrated in a cross-section and top view of the switch in Fig. 9a and b. The dielectric is silicon nitride with a thickness of 0.5 lm and a dielectric constant of 6 and serves to prevent the electric short between two conductors, providing at the same time a low impedance path for the RF signal. The mechanical part (membrane) is made of aluminum and is 1 lm thick, 200 lm long. The top electrode is suspended by a spring and can be pulled down by applying a bias (voltage) across the air gap between the between the membrane and the bottom gold electrode. Above a certain voltage, the balance between the attracting electrostatic force Fe and restoring spring force Fspring becomes unstable and the switch closes (device is in the off state). This explains the sudden increase in the capacitance of the switch Fig. 12. The switch can be only open again (the membrane springs back to its fully suspended position) if the bias is lower than the so-called Vpullout. The

Fig. 11. Bias voltage waveforms.

Fig. 12. Bias voltage and capacitance over time after each stressed cycle.

two voltages Vpullin and Vpullout can be determined by tracing (measuring) the hysteresis C–V curve Fig. 13. 6.2. Test bench

Fig. 9. (a) Top view of RF MEMS capacitive switch and (b) cross-section view (not to scale) of the capacitive switch. Bias voltage is applied between the three bottom electrodes and the membrane.

The dielectric’s switch reliability has been studied using the test bench presented in Fig. 10. This setup allows plotting the evolution of the Vpullin bias voltage over time for a given stress. It is composed

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lows getting the V and C data. Once the data has been stored, it is treated to extract Vpullin for each measure to trace the Vshift evolution over time Fig. 14. 7. Conclusions A novel reliability model for capacitive RF MEMS is presented. The model combines the failure analysis and device functionality. The VHDL-AMS language is used due to its multi-scale multi-physics capabilities that allow introducing both the device functionality and physics. This paper focuses on a step in a methodological procedure which consists in modeling a physical process evolving in time and identified as responsible for device failure. The model takes into account environmental conditions and device usage. This dual modeling is then introduced into a system model to produce a ‘‘reliability model” which will give by simulation an estimate of the functional life of the device (MEMS) i.e. predict the expected life time for a defined mission profile.

Fig. 13. C–V curves after each stressed cycle.

References Voltage (V)

2

0 100

Time (s)

1000

10000

Fig. 14. Measured pull-in shift voltage over time.

by a programmable arbitrary function generator (AFG), used to apply different bias voltages to the RF switch via the probe and a Capacitance Meter that measures the switch capacitance. The AFG and the Capacitance Meter outputs are, respectively, connected to the channel 1 and channel 2 of the Oscilloscope (OSC), allowing us to trace the C(t), V(t) curves Fig. 12. To test the lifetime of a RF MEMS switch, the switch must be repeatedly actuated until failure. The simplest method to monitoring switch actuation is to apply a continuous wave signal to the switch and measure the shift of the C–V curve Fig. 13. A LabWindows-CVI program was written to automate (remote control the three instruments through the GPIB bus) the test bench. It stresses the switch and periodically measures C and V. The applied voltage waveforms are shown in Fig. 11. They consist in stress signals combined with a positive triangular signal that al-

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