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Piezoelectric Coefficients of Thin Film Aluminum Nitride Characterizations Using Capacitance Measurements Mahmoud Al Ahmad, Member, IEEE, and Robert Plana, Member, IEEE
Abstract—Piezoelectric materials have become very useful in MEMS devices because of their electrical-mechanical reciprocity. Aluminum nitride has attracted considerable attention in recent years owing to its unique properties. Here we report for the determination of aluminum nitride (AlN) piezoelectric thin film charge constants. When voltage is applied, the AlN film geometrical dimensions will change. The proposed technique does this determination by taking the ratio of parallel plate capacitance for two different bias conditions under set of assumptions in deriving the equations for the ratio of capacitance for the two bias conditions.
TABLE I COMPARISON BETWEEN VARIOUS PIEZOELECTRIC MATERIALS
Index Terms—Aluminum nitride (AIN), characterizations, dimensional variation, material parameters, piezoelectric material.
I. INTRODUCTION
T
HE high frequency of operation inherent in microelectromechanical systems (MEMS) devices matches well with the relatively high frequency capability of piezoelectric materials. The most commonly used piezo-materials in MEMS devices are lead zirconate titanate (PZT), zinc oxide (ZnO), and aluminum nitride (AlN). Aluminum nitride has attracted considerable attention in recent years owing to its unique properties. Specifically, its high thermal conductivity, moderate piezoelectricity, low dielectric and acoustic losses and high acoustic wave velocity have made highly textured AlN thin films a prime candidate for electro-acoustic applications such as filters, resonators, and sensors. A comparison between various piezoelectric materials is summarized in Table I. Therefore, it has become increasingly important to characterize the activity of piezoelectric materials under conditions relevant to such applications. Consequently different methods have been sought to measure the piezoelectric activity [1]–[7]. Nevertheless these techniques and their results still need further understanding and validation. Recently we have presented in [8] a promising method of measuring the vertical extension of a piezoelectric thin film using an impedance analyzer. This work reports the characterization of aluminum nitride (AlN) piezoelectric thin film dimension variations when dc bias is applied. AlN does not require any polling process due to its ori-
Manuscript received August 04, 2008; revised November 24, 2008. Current version published March 11, 2009. The authors are with LAAS-CNRS, University of Toulouse, Toulouse 31077, France (e-mail:
[email protected];
[email protected]). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LMWC.2009.2013682
Fig. 1. AlN piezoelectric response to applied field. d is perpendicular to the cylindrical surface aligned with the direction of the applied field and d is parallel to the surface. E is equal to V =d. (a) no bias, (b) under bias.
ented structure. The determination of the variation in the longitudinal and transversal directions is the key for the characterizing a piezoelectric film parameters, namely, its strain and charge constants. II. THEORY AND ANALYSIS The capacitance of a dielectric film is given by the equation [9] (1) where is the permittivity of vacuum, is the relative permittivity or dielectric constant, is the thickness of the film, and is the area of the capacitor. Having measured the capacitance of an AlN film, (1) can be used to find the electronic dielectric constant. Fig. 1(a) shows a solid circular piece of a AlN piezoelectric material. When the circular solid is driven with the application of a dc field [Fig. 1(b)] it will cause its material do-
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AL AHMAD AND PLANA: PIEZOELECTRIC COEFFICIENTS OF THIN FILM ALUMINUM NITRIDE CHARACTERIZATIONS
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mains to contract, therefore the thickness of the film increases while the area decreases by [10]. Moreover, both the by , and the variation in vertical extension of the AlN material area , are correlated with the magnitudes of both the longi, and the transverse charge constants as follows tudinal [10]: (2) (3) Moreover (4) where
lies between 2 and 2.5 [11]. Thus
Fig. 2. Fabricated AlN parallel plate capacitor.
(5) The modification in the material shape is translated into a change in the capacitance value; which is approximately calculated through the well known capacitance parallel plate formula (6) rewrite (6) as follows: (7) Hence (8) Inserting (5) into (8) and solving for tively, yields
and
, respec-
(9) (10) where is the ratio between and . The piezoelectric material is activated with the application of a dc field and the capacitance will decrease due to the change in the geometrical dimensions as predicted by (2) and (3). Hence, knowing the thin film thickness and the capacitance ratio will enable the vertical/horizontal extension of the piezoelectric material to be determined.
Fig. 3. AlN capacitance versus frequency (logarithmic scale): C is the unbiased capacitance and C is the capacitance with the application of 2 V.
a first experimental evidence of the theory presented above. That is applying a dc bias yields the expansion of the material due to the converse piezoelectric effect. Thus cause a decrease in the capacitance yielded by this structure as clearly depicted in Fig. 3. The amount of variation in capacitance due to the application of dc bias is around 3.5% from its unbiased value. From (9) and (10), the data of Fig. 3 and by using (2) and and , the piezoelectric coefficients versus (3) to compute frequency are computed and are shown in Fig. 4. Fig. 4 reveals pm/v and 1.7 pm/v that 4.1 pm/v pm/v, respectively [12].
III. MEASUREMENTS AND ANALYSIS A parallel plate capacitor composite of AlN piezoelectric material has been fabricated and is shown in Fig. 2. The capacitor dielectric material is composed of AlN thin film of thickness 0.6 m. The electrodes are made from Molybdenum with thickness of 0.1 m. The capacitor has an area of 700 200 m . The capacitances of the fabricated device with and without dc bias were measured with the HP4294A impedance analyzer and are shown in Fig. 3. The measurements show a stable and smooth behavior over the frequency. These results represent
IV. VALIDATION AND ERROR ESTIMATION The AlN material tested in this work have been measured. A “Take Control” piezometer was used to measure the coefficient utilizing Berlincourt technique in [13]. The measured value was 5.7 pm/V. This value obtained by the Berlincourt method lies in the computed range obtained by the current technique. However, assuming the computed mid range value of to be the real material parameter, then estimation error will be 14%.
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capacitance ratio is taken. Thus, the extracted parameters of the current technique is much higher than that material parameters obtained by the other existing methods. V. CONCLUSION
Fig. 4. Piezoelectric coefficients magnitudes versus frequency.
For extra validations, the free beam is actuated and the deflection of the beam was measured at its tip using the interferometry system from FOGALE Nanotech [14]. Full field 3D non-contact surface measurements based on optical interferometry is used to measure the tip displacement of the free end moveable AlN cantilever. The surface of the silicon substrate is assigned as a zero-reference. The traveling distance of the tip is found to be around 18 m when 2 V is applied. The traveling direction is away from the substrate. The extracted measured using the multilayer beam model developed in [15] is 2.5 pm/V. Comparing this value with the computed one, it also located in the range between 1.7 pm/V and 4.3 pm/V. Again, assuming the to be the real material paramcomputed mid range value of eter, then estimation error will be 16%. Now, the real value for , i.e., is equal 2.28. Considthe material of this work is ering the simplicity of the introduced method and the difficulty of the task this represents a very satisfactory and promising approach. As we have stated previously in this letter, it is not an easy task to absolutely decide which one is the most representative technique. The use of mechanical devices looks quick and easy solution. However, with the need of high precision poses a problem. Direct measurement of induced charge becomes problematic for thin films because the properties of metallic contacts used to apply the force and collect the piezoelectric charge. The resonance techniques are based on assumption that samples are infinitely thin or infinitely long, and the corrections for finite dimensions must be taken into account. Moreover, the relationship of resonant and antiresonant frequencies to the piezoelectric and elastic properties of the films becomes less certain. In optical techniques the sample is constrained by the substrate whose eventual deformation by the applied field must be considered. Furthermore, the interfacial capacitance between the metallizations and the AlN film is automatically deembedded when the
This letter is devoted to the development of an original method using the electromechanical properties of the piezoelectric material, specifically the AlN thin film. This method avoids the use of complicated test set as well as complex sample preparation. The interfacial issues between the metallizations and the AlN film is automatically deembedded when the capacitance ratio is taken. The current technique results in a higher value compared with other existing methods. The real values of the coefficients are located in the computed range. Assuming the computed mid range value to be the real material parameter, then estimation error will be 16%. As have been stated, it is not an easy task to absolutely decide which one is the most representative technique. REFERENCES [1] R. N. Torah, S. P. Beeby, and N. M. White, “Experimental investigation into the effect of substrate clamping on the piezoelectric behavior of thick-film PZT elements,” J. Phys. D: Appl. Phys., vol. 37, pp. 1074–1078, 2004. [2] D. Royer and V. Kmetik, “Measurement of piezoelectric constants using an optical hetrodyne interferrometer,” Electron. Lett., vol. 28, no. 19, pp. 1828–1830, 1992. [3] P. Muralt, “Ferroelectric thin films for micro-sensors and actuators: A review,” J. Micromech. Microeng., vol. 10, pp. 136–146, 2000. [4] J. F. Shepard, P. J. Moses, and S. Trolier-McKinstry, “The wafer flexure technique for the determination of the transverse piezoelectric coefficient (d(31)) of PZT thin films,” Sensors Actuators A, vol. 71, pp. 133–338, 1998. [5] D.-G. Kim and H.-G. Kim, “A new characterization of piezoelectric thin films,” Appl. Ferroelect., pp. 65–68, 1998. [6] Z. Yuxing, W. Zuoqing, and J. D. N. Cheeke, “Resonant spectrum method to characterize piezoelectric films in composite resonators,” IEEE Trans. Ultrason., Ferroelect. Freq. Control, vol. 50, no. 3, pp. 321–333, Mar. 2003. [7] B. Gautier, S. Ballandras, V. Blondeau-Patissier, W. Daniau, D. Hauden, and J. C. Labrune, “Contribution to the understanding of quantitative measurements of piezoelectric coefficients of thin films using AFM piezoresponse mode,” Appl. Ferroelect., pp. 99–102, 2002. [8] M. Al-Ahmad and R. Plana, “A novel method for PZT thin film piezoelectric coefficients determination using conventional impedance analyzer,” in Proc. 37th Eur. Microw. Conf., Munich, Germany, Oct. 2007, pp. 202–205. [9] B. C. Wadell, Transmission Line Design Handbook. Norwood, MA: Artech House, 1991. [10] N. N. Rogacheva, The Theory of Piezoelectric Shells and Plates. Orlando, FL: CRC, 1994. [11] B. Jaffe, W. R. Cook, and H. Jaffe, Piezoelectric Ceramics. Marietta, OH: R. A. N. Publishers, 1971. [12] M. M. Wong, U. Chowdhury, D. Sicault, D. T. Becher, J. C. Denyszyn, T. G. Zhu, M. Feng, and R. D. Dupuis, “Delta-doped AlGaN/A1NGaN microwave HFETs grown by metalorganic chemical vapour deposition,” Electron. Lett., vol. 38, no. 9, p. 428, 2002. [13] [Online]. Available: http://www.piezotest.com [14] [Online]. Available: http://www.fogale.fr [15] D. L. DeVoe and A. P. Pisano, “Modeling and optimal design of piezoelectric cantilever microactuators,” Trans. ASME, J. Micro Electromech. Syst., vol. 6, no. 3, pp. 266–270, Sep. 1997.
