A Test Structure for Young Modulus Extraction through Capacitance-Voltage Measurements Jize Yan and Ashwin A. Seshia

Peter Steeneken and Joost Van Beek

Department of Engineering University of Cambridge Cambridge, United Kingdom

Philips Research Laboratories 5656AA Eindhoven, The Netherlands

Abstract—We present a test structure for the on-line extraction simultaneous resonant frequency tests and measurement of of the Young’s modulus of materials used for Micro-Electro- pull-in voltage, thereby allowing for a multi-point orthogonal Mechanical Systems (MEMS) applications. This non-contact measurement. method is simple and non-destructive and allows for a fully electronic probing and readout. A single test structure is configured to respond to a change in voltage through a change in capacitance and the change in capacitance is then related to the Young’s Modulus and the device geometry. The device can also be used for simultaneous resonant frequency tests and measurement of pull-in voltage, thereby allowing for a multipoint orthogonal measurement. Experimental verification of the concept is presented in this paper. The test structure is fabricated in a silicon-on-insulator MEMS process allowing the extraction of the Young Modulus of [110] single-crystal silicon.

I.

INTRODUCTION

The monitoring of the mechanical properties of MEMS materials is required for monitoring and refining of fabrication processes for MEMS and for the design of mechanical sensors and actuators based on MEMS technology. The Young’s Modulus is an important material parameter required for the design of micro-electromechanical devices comprised of beams and plates. Previous methods to extract Young’s Modulus include surface profilometry on cantilever beams [1, 2], resonance frequency measurements on beam structures [3] and pull-in voltage measurements on arrays of beam-like structures of defined geometries [4]. All of these methods typically require measurement of critical dimensions and a measurement across an array of structures for improved estimates. Accurate (electro-)mechanical models are additionally required for numerical extraction of the Young’s Modulus. In this work, we present a method for the extraction of the Young’s Modulus from a single device. This non-contact method is simple and non-destructive in nature and allows for a fully electronic probing and readout. A single test structure is configured to respond to a change in voltage through a change in capacitance and the change in capacitance is then related to the Young’s Modulus and the device geometry. The device can also be used for

DESCRIPTION

The device consists of an electrostatically actuated beam connected to a variable capacitor as shown schematically in Fig. 1. A parallel plate actuator is used to drive the beam at a specified frequency. The deflection of the beam in response to the voltage-controlled electrostatic force is coupled as a change in capacitance of the variable capacitor. The measured capacitance as a function of voltage depends on the geometric and materials properties of the deflecting beam and the topology of the actuator and the variable capacitor. A measurement of the change in capacitance of the variable capacitor as a function of voltage together with can yield an estimate of the Young’s Modulus. The estimate can be improved if the critical dimensions are measured postprocess.

Figure 1. Schematic of the test structure. The capacitance of a variable capacitor attached to an electrostatically actuated beam gives a measure of the Young’s Modulus.

This work is supported by the EU FP6 project #IST-2003-507914. 0-7803-9056-3/05/$20.00 © 2005 IEEE.

II.

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oxide is sacrificed using a timed buffered HF etch to obtain released structures.

We can write down three equations to relate the Young’s Modulus to beam deflection for the idealized device.

Fe =

ε o Te LeV p2 2( g − x ) 2

Actuator electrode

(1)

Equation (1) relates the actuator force, Fe, to the displacement of the structure (x) and the actuator voltage (Vp). The geometry of the actuator is defined by the overlap area of the electrodes and effective gap as given by the width, Te, and length, Le and the nominal gap, g.

Deflecting beam

The compliance of the actuated beam can be expressed as a function of the Young’s Modulus and the geometry of the beam. Thus, the Young’s Modulus can be related to the deflection of the actuated beam by Equation (2):

Variable capacitor

E=

Fe L3

192 xI z

(2)

Here, L is the length of the beam and Iz is the second moment of area of the beam about an axis passing perpendicular through the plane of Fig. 1. Finally, the deflection of the beam is measured using the variable capacitorx ∆C ≅ g C

Figure 2. Optical Micrograph of test structure realised in a SOI-wafer based process. Device dimensions are roughly 400µm x 800µm. Contact pads are not shown.

(3)

An optical micrograph of a sample fabricated device is shown in Fig. 2. The capacitance of the variable capacitor can be extracted by various techniques. For the measurements reported herein, a network analyzer is used to measure the admittance of the device as a function of the DC voltage between the actuator and the deflecting beam. The sense capacitance is then extracted from the measured admittance numerically. A schematic of this test setup is shown in Fig. 3.

Here ∆C is the change in capacitance of the variable capacitor and C is the nominal capacitance. Thus, equations (1)-(3) together can be used to obtain the Young’s Modulus of the structure from the measured C-V characteristic of the device. Greater accuracy can be obtained by using more accurate forms of the above equations to account for non-idealities in the operation of the test structure and also by measurement of critical dimensions post-process.

III.

EXPERIMENT

An array of test structures has been fabricated in a three mask SOI-wafer based process. The starting substrates are 6” (100) SOI wafers comprising of a 20µm thick device layer, a 2µm thick buried oxide and a 675µm thick handle wafer. The resistivity of the p+ device layer is under 0.015Ω/cm. The minimum feature size limited by lithography is 2µm. Aluminum metallization is used for interconnect. Deep reactive ion etching of silicon is used to define the electrode gaps and critical features in the device layer. The buried

Figure 3. Measurement setup to obtain the C-V characteristic of the device connected in a two-port configuration.

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It is apparent from the schematic of the test setup, that the measurement of the admittance of the device will include not only the variable capacitance, but also electro-mechanical parasitics. In Fig. 3, C12 represents the capacitance of the variable capacitor, C1s and C2s are the capacitances between the electrodes and the substrate and Cgs represents the capacitance between the substrate and ground. It is required to cancel the effect of these parasitic elements to improve the accuracy of the measurement technique. We have chosen to do a numerical cancellation; with a grounded substrate it is expected that the results will further improve. The measured frequency response of the device over a range 2-10 MHz is plotted in Fig 4. The contribution of mechanical resonances to the measurement is limited by the damped response of the mechanical modes associated with the motion of the structure at these frequencies.

An average value of Young’s Modulus is found to be approximately equal to 162 GPa. Further measurements are underway to infer the statistical merit of this technique.

IV.

The test structure presented has the potential to combine three different methods for the estimation of material properties within a single device. While the measurement setup described in this paper is an indirect method to extract capacitance, it is possible to build custom interface circuits to measure the capacitance of the variable capacitor very precisely by leveraging off the development of highaccuracy MEMS capacitive sensors [5]. Other techniques can also be used; for instance a conventional LCR meter found in most electronics laboratories could be used for capacitance measurement. Measurements of critical dimensions of the fabricated structure will limit the error in the estimate of the Young’s Modulus. Future experimental work is expected to include more detailed testing on the device including a ramping of the voltage over smaller increments, pull-in measurements and measurement of resonant frequencies of mechanical modes associated with the motion of the structure. With additional data, it will be possible to infer statistical measures of accuracy for this method.

Normalized gain

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DISCUSSION

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V.

ACKNOWLEDGMENTS

Acknowledgments are due to Suat Ayoz and Hatice Tuncer, both currently affiliated with the Department of Engineering at Cambridge University, for assistance with the measurements on the test structure.

Frequency (Hz) Figure 4. Frequency response of the voltage-controlled variable capacitor.

Using an analysis similar to that described in section II, we can estimate the Young’s Modulus from the measurements shown in Fig. 4. The results allow for an estimate of the Young’s Modulus of [110] silicon.

REFERENCES [1]

Young’s Modulus (Pa)

[2]

M. W. Denhoff, ‘A measurement of Young’s modulus and residual stress in MEMS bridges using a surface profiler’, J. of Micromechanics and Microengineering, vol. 13, no. 5, pp. 686-692, 2003. Y-C Tai and R S Muller, ‘Measurement of Young’s modulus on microfabricated structures using a surface profiler’, Proc. IEEE

Micro Electro Mechanical Systems Workshop (Napa Valley, CA) pp 147–52, 1990. [3]

[4]

[5]

Voltage (V) Figure 5. A plot of the estimate for Young’s Modulus extracted from measurements in Fig. 4.

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L. Kiesewetter, J.-M. Zhang, D. Houdeau, and A. Steckenborn, ‘Determination of Young’s moduli of micromechanical thin films using the resonance method’, Sensors and Actuators A, vol. 35, no. 2, p. 153, 1992. P. Osterberg and S. D. Senturia, ‘M-TEST:A Test Chip for MEMS Material Property Measurement Using Electro-statically Actuated Test Structures’, IEEE/ASME J. of Microelectromechanical Systems, vol. 6, no. 2, p. 107, 1997. J.R. Geen, S.A. Sherman, J.F. Chang and S.R. Lewis, ‘Single-chip surface micromachined integrated gyroscope with 50/spl deg//h Allan deviation’, IEEE J. of Solid State Circuits, vol. 37, no. 12, pp. 186066, 2002.