Time and voltage dependence of dielectric charging in RF MEMS capacitive switches R.W. Herfst1 , P.G. Steeneken1 , and J. Schmitz2 1

NXP Semiconductors High Tech Campus 5 (Postbox WAY41), 5656 AA Eindhoven, The Netherlands. Phone: +31 (0)40 2745252 Fax: +31 (0)40 2744113. E-mail: [email protected]. 2 MESA+ Research Institute, Chair of Semiconductor Components, University of Twente. P.O. Box 217, 7500 AE Enschede, The Netherlands.

Abstract— A major issue in the reliability of RF MEMS capacitive switches is charge injection in the dielectric. In this study we try to establish the time and voltage dependence of dielectric charging in RF MEMS with silicon nitride as a dielectric. It is shown that√the voltage shift of the CV-curve due to injected charge shows a t dependence over a large time range. By doing measurements on a large number of devices (early development material made at NXP Semiconductors in Nijmegen) we further show that the charging rate increases exponentially with the applied stress voltage. Index Terms— RF MEMS, capacitive switch, dielectric, charging, reliability, silicon nitride.

I. I NTRODUCTION RF MEMS (Radio Frequency Micro-Electro-Mechanical Systems) capacitive switches show great potential for use in wireless applications. Desirable aspects are the good RF characteristics (such as high linearity and low losses) and the low power consumption [1]. However, obtaining a high reliability is a major challenge for the successful implementation of the switches in commercial products. The most important mechanism that causes degradation of the switch is the injection and trapping of charge into the dielectric layer due to the applied electric field [1]–[7]. The injected (and subsequently trapped) charge redistributes the internal E-field and results in a built-in voltage that shifts the CV-curve of the device [6]–[8]. This shift may even be large enough to cause the pull-out voltage to shift past V = 0, after which the device will not open when the bias voltage is removed. Experiments have shown [2], [9], [10] that the shift in the CV-curve increases with time and stress voltage, but the exact mechanism and time behavior are not known. Although several models for the time and stress voltage dependence of the voltage shift have been proposed, the experimental verification of these models was usually done on a limited number of samples and/or over a small voltage and time range. In this study we present new measurement data obtained on early development material made at NXP Semiconductors in Nijmegen with a fast capacitance measurement setup, which allows accurate measurements of changes in the CV-curve over a wide time and voltage range. From these data we conclude

Springs

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Schematic representation of an RF MEMS capacitive switch.

that the time and voltage dependence √ of the shift in the CVcurve are described by Vshift = α t exp (βVstress ). II. S WITCHING BEHAVIOR AND EFFECT OF CHARGE INJECTION

A schematic representation of an RF MEMS capacitive switch is shown in Fig. 1. The switch consists of two electrodes, a dielectric layer (silicon nitride, 425 nm thick) and an air gap. The top electrode is suspended by springs. In our case the electrode material is an AlCu alloy, and the dielectric is a silicon nitride with a thickness of 425 nm. When a voltage is applied across the two electrodes, the electrostatic force FE will pull the electrode downward until it is in equilibrium with the restoring mechanical spring force Fspring . Above a certain voltage, called the pull-in voltage Vpi , the balance between FE and Fspring becomes unstable and the switch closes, which is marked by a sudden increase in the capacitance. Since the distance between the two electrodes is relatively small in this position, the electrostatic force is larger than the restoring force in the closed state, so that when the voltage is decreased again, the switch will not open at V = Vpi but at a lower voltage, the pull-out voltage Vpo . As the electrostatic force is proportional to the voltage squared, this pull-in and pull-out behavior is present for both positive and negative voltages. When the switch is in the closed position, an electric field of the order of typically 1 MV/cm is present. Due to this field charge is injected and trapped in the dielectric, causing a change in the electric field. The net effect of the trapped

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Fig. 2. CV-curve before (black) and after (grey) it has been stressed at 60 V for 300 seconds. a) The voltage of minimal capacitance shifts to the right due to trapped holes. b) Narrowing of the CV-curve. c) Combined effect of both shifting and narrowing of the CV-curve is visible.

charges is thus a built-in voltage Vshift which shifts the CVcurve [5]–[8]. In Fig. 2a this can be observed as a change in the voltage at which the CV-curve is minimal. Vshift is proportional to the amount of injected charge: positive charge will shift the CV-curve to the right, negative charge shifts it to the left. The position of the injected charge is also important: injected charge located close to the surface of the dielectric is more important than charge located near the bottom electrode, because the effect of charge near the bottom electrode is less due to mirror charges in the electrode [5]. Another effect that can take place is a narrowing of the CVcurve (see Fig. 2b) [9]. An explanation [11] for the narrowing effect is that charge may not be homogeneous in the lateral direction. If this is the case, the inhomogeneous field can not be completely cancelled by the homogeneous applied field caused by the bias voltage. The result is that there is always an electrostatic force, so that the pull-in and pull-out voltages nive closer together. An example of the combined effect of shifting and narrowing is shown in Fig. 2c. Both shifting and narrowing of the CV-curve cause reliability problems when one of the pull-out voltages shifts past V = 0: a closed switch will not open again when the bias voltage is set to zero. III. M EASUREMENT METHOD AND SETUP The experiments consist of a constant-voltage stress, interrupted at increasing time intervals for a low-voltage measurement of the CV-curve shift. We determine Vshift by fitting a parabola C(V ) = c · (V − Voff )2 + Cmin through the central

part of the CV-curve. Voff is then the voltage at which the capacitance has the lowest value (Fig. 2a). At V = Voff , the applied electric field cancels the electric field in the gap caused by the trapped charges, resulting in the smallest capacitance value. We then define the voltage shift Vshift (t) as Voff (t) − Voff (t = 0). In a previous study [12], we showed that this lowvoltage measurement method causes less device degradation than conventional CV tests. An additional advantage is that CV-curve narrowing will not affect the determination of Vshift , which makes it possible to study shifting and narrowing seperately. The measurements are conducted on unpackaged devices, with a dry N2 flow to prevent adverse effects due to moisture. Capacitances are measured with an 1-port RF measurement system based on the description given by Nieminen et al. [13] which is schematically depicted in Fig. 3. It works as follows: an RF signal from a signal generator is split in two. One part goes into the local oscillator of the IQ-demodulator. To the other part a DC bias is added. The signal passes through a circulator and reflects back from the RF MEMS capacitive switch. The reflected signal passes through the circulator and a 100 pF decoupling capacitor to the RF-in port of the IQdemodulator. The amplitude and phase of the reflected signal are determined from the I and Q signals using an oscilloscope. A 10-dB attenuator (Fig. 3) minimizes the effect of small nonlinearities in the IQ-demodulator. By first doing an open-shortload calibration, the capacitance can be calculated from the measured reflection. The capacitance measurement speed is very fast, and the CV-curve measurement time is limited by the

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Vshift (t) = Vmax · (1 − exp (−kt)) + V0 √ Vshift (t) = a t + V0 ¡ ¡ ¢¢ Vshift (t) = Vmax · 1 − exp −ktδ + V0 .

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at a fixed stress voltage. Spengen et al. [5], Yuan et al. [10], and Papaioannou et al. [14] describe charge build-up in the dielectric with an exponential time dependence indicating a fixed amount of traps which are slowly filled by the leakage current. Since in the closed state the capacitive switch is similar to a MIM capacitor, reliability literature on these devices may also offer relevant models. Lau et al. [15], Shannon et al. [16], van Delden et al. [17], and Street [18] link degradation of amorphous silicon and silicon nitride to the generation of metastable defects by currents, with mechanisms related to light-induced changes in amorphous silicon [19], [20]. They find that the defect density is proportional to the square root of t. Redfield et al. [21] interpret generation of metastable defects in another way and propose a stretched-exponential time dependence. Hence, we compare the three following time evolutions of Vshift :

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Fig. 4. Measured Vshift as function of stress time. Vstress : 40 V. a) Linear axes. b) Double Logarithm axes with three different fit function.

mechanical response time of the MEMS: if the measurement is performed too quickly, the flanks at pull-in and pull-out in the CV-curve are not vertical. To rule out this effect, we measure a CV-curve in 400 ms. IV. M EASUREMENTS AND INTERPRETATION In Fig. 4a an example of the measured Vshift as function of stress time is given. On a double-logarithmic scale (Fig. 4b), the points are approximately on a straight line with a slope around 0.56. It is therefore tempting to follow previous works in using a few-parameter model to describe the behavior of Vshift (t)

(1) (2) (3)

In these equations Vmax , k, a and δ may all depend on the stress voltage and temperature. The extra fit parameter V0 was added to each model to account for small systematic errors in the determination of Vshift - induced e.g. by the limited accuracy of the Voff (0) measurement value. The data in Fig. 4b lie approximately on a straight line with slope 0.56, which hints in the direction of the square root behavior also found in the degradation of MIM capacitors. If √ we fit the function Vshift (t) = a t + V0 to the data we get a good agreement between the measurement data and the fitting result (see Table I). The accuracy of each Vshift data point from the parabolic fit procedure amounts to 30 mV. Additional unquantified fluctuations include temperature variations (on very long time scales correlation between charging speed and temperature changes due to day/night cycles were observed) and relaxation of the injected charge during the determination of Vshift (on short time scales the time it takes to determine Vshift becomes comparable to the stress time between two data points). The fit with model 1 suggests that the overall error per measurement is 50 mV. The fitted value of V0 is 39 ± 15 mV, which is small enough to be compatible with the notion that it is only added to account for the small systematic error made due to the limited accuracy of Voff (0). In table I, the fit results of the other two models are also presented. The χ2 /D.O.F. is a measure of the distance of the points to the curve (normalized to the measurement error) and a lower value objectively indicates a better fit, even if the measurement error is not known exactly. Clearly, the exponential fit (model 1) gives a poor description of the data, while the other two models are satisfactory. However, the stretched-exponential equation fit does not converge to a final result: while δ converges to 0.53 ± 0.03, Vmax and k turn out to be highly correlated, with k very small and Vmax very large.

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TABLE I F ITTING RESULTS OF THE MEASUREMENT DATA DISPLAYED IN F IG . 4 B

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√ t for stress voltages ranging

Since k is very small a Taylor expansion can be performed on (3): ¡ ¡ ¢¢ Vshift (t) =Vmax · 1 − exp −ktδ = ¡ ¢ Vmax · ktδ + O(k 2 t2δ ) . (4) If δ = 0.5, Vmax = a/k, and take the limit of k → 0, the stretched exponential is equal to (2). This indicates that the stretched exponential is in the limit where it converges to the square root function. We conclude that a stretched exponential is an unneccesary generalization of model 2 for these data. The square-root model seems preferable, because of its good correspondence to the data and its simplicity. To verify if √ measurements at different stress voltages √show the same t behavior, we plot Vshift as function of t for different voltages. This is shown in Fig. 5. For clarity, only 8 out of 62 measurements are shown here. The model holds well over the entire stress-bias regime, while it is again evident that the error-bars are somewhat underestimated. From all 62 charging measurements the slope a of the square root time dependence was obtained. It is plotted as a function of stress voltage in Fig. 6. Although there is quite some spread from device to device, from this graph it is clear that within the range of stress voltages the slope increases exponentially with V . This is in agreement with previous results which state that the lifetime decreases exponentially with V . We thus find that the time and voltage behavior of dielectric charging

in RF MEMS capacitive switches can be described with the straightforward equation: √ Vshift (t) = α t exp (βVstress ) , (5) for which in our case α ' 2.4 · 10−4 V/s1/2 and β ' 0.12 V −1 . V. C ONCLUSIONS A thorough investigation of the charge injection in RF MEMS capacitive switches is presented. We collected a large amount of measurement data using a refined stress-measure sequence. The dielectric charging, expressed as the voltage shift of the minimum capacitance value, shows a dependence with the square-root of time and the exponent of stress voltage over a wide range of stress conditions. This is a strong indicator that dielectric charging is governed by charge trapping in current induced metastable defects, which is also responsible for changes in the conductivity of silicon nitride MIM capacitors. ACKNOWLEDGEMENTS We thank our colleagues at NXP Semiconductors Nijmegen for providing samples of the RF MEMS capacitive switches and fruitful discussions on RF MEMS reliability. R EFERENCES [1] Gabriel M. Rebeiz, RF MEMS - Theory, Design, and Technology, John Wiley & Sons, Inc, 2003. [2] S. Melle, E Flonrens, D. Dubuc, K. Grenier, P. Pons, F. Pressecq, 1. Kuchenbecker, J. L. Muraro, L. Bary and R. Plana, Reliability overview of RF MEMS devices and circuits, 33rd European Microwave Conference, vol. 1, pp. 37-40, October 2003. [3] C. Goldsmith, J. Ehmke, A. Malczewski, B. Pillans, S. Eshehnan, Z. Yao, J. Brank and M. Eberly, Lifetime characterization of capacitive RF MEMS switches, 2001 IEEE MTT-S Int. Microwave Symp. Digest, vol. 1, pp. 227-230, May 2001. [4] J. DeNatale, R. Mihailovich and I. Waldrop, Techniques for reliability analysis of MEMS RF switch, 40th Annual IRPS, pp. 116-117, April 2002.

[5] W. Merlijn van Spengen, Robert Puers, Robert Mertens, and Ingrid De Wolf, A comprehensive model to predict the charging and reliability of capacitive RF MEMS switches, J. Micromech. Microeng. vol. 14, 514521, 2004. [6] J.R. Reid, Dielectric charging effects on capacitive MEMS actuators, 2002 IEEE MTT-S Int. Microwave Symp. Digest, RF MEMS workshop, June 2002. [7] S.S. McClure, L. D. Edmonds, R. Mihailovich, A.H. Johnston, P. Alonzo, J. DeNatale, J. Lehman, and C. Yui, Radiation effects in microelectromechanical systems (MEMS): RF Relays, IEEE Trans. On Nuclear Science, vol. 49, no. 6, December 2002. [8] I. Wibbeler, G. Heifer and M. Hietschold, Parasitic charging of dielectric surfaces in capacitive microelectromechanical systems (MEMS), Sensors and Actuators A: Physical, pp. 74-80, November 1998. [9] J.R. Reid, and R.T. Webster, Measurements of charging in capacitive microelectromechanical switches, ELECTRONICS LETTERS, vol. 38, no. 24, 21st November 2002. [10] Xiaobin Yuan, James C.M. Hwang, David Forehand, and Charles. L. Goldsmith, Modeling and characterization of Dielectric-Charging Effects in RF MEMS Capacitive Switches, 2005 IEEE MTT-S Int. Microwave Symp. Digest. [11] X. Rottenberg, B. Nauwelaers, W. De Raedt, and H.A.C. Tilmans, Distributed dielectric charging and its impact on RF MEMS devices, 34th European Microwave Conference - Amsterdam, 2004. [12] R.W. Herfst, H.G.A. Huizing, P.G. Steeneken, and J. Schmitz, Characterization of dielectric charging in RF MEMS capacitive switches, 2006 IEEE International Conference on Microelectronic Test Structures, 133136, 6-9 March 2006. [13] H. Nieminena, J. Hyyryl¨ainen, T. Veijola, T. Ryh¨anen, V. Ermolov, Transient capacitance measurement of MEM capacitor, Sensors and Actuators A, vol. 117 (2005), 267272. [14] Giorgos Papaioannou, Michael-Nicolas Exarchos, Vasilios Theonas, Guoan Wang, Student Member, IEEE, and John Papapolymerou, Senior Member, IEEE, Temperature Study of the Dielectric Polarization Effects of Capacitive RF MEMS Switches, IEEE Transactions on Microwave Theory and Techniques, vol. 53, no. 11, 3467, november 2005. [15] S.P. Lau, J.M. Shannon, Generation and annealing kinetics of current induced metastable defects in amorphous silicon alloys, Journal of NonCrystalline Solids, vol. 266-269 (2000), 432-436. [16] J.M. Shannon, S.C. Deane, B. McGarvey, and J.N. Sandoe, Current induced drift mechanism in amorphous SiNx : H thin film diodes, App. Phys. Lett., vol. 65, 5 December 1994. [17] M.H.W.M. van Delden and P.J. van der Wel, Reliability and electric properties for PECVD A − SiNx : H films with an optical bandgap ranging from 2.5 to 5.38 eV, IEEE 41st Annual International Reliability Physics Symposium, Dallas, Texas, 2003. [18] R.A. Street, Current-induced defect creation and recovery in hydrogenated amorphous silicon, Appl. Phys. Lett., vol. 59 (9), 26 August 1991. [19] M. Stutzmann, W.B. Jackson, C.C. Tsai, Light-induced metastable defects in hydrogenated amorphous silicon: A systematic study, Phys. Rev. B, vol. 32, 23-47, 1985. [20] D.L. Staebler and C.R. Wronski, Reversible conductivity changes in discharge-produced amorphous si, Appl. Phys. Lett., vol 31, 292, 1977. [21] D. Redfield, and R.H. Bube, Reinterpretation degradation kinetics of amorphous silicon, Appl. Phys. Lett., vol. 54 (11), 13 March 1989.