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PROC. 29th INTERNATIONAL CONFERENCE ON MICROELECTRONICS (MIEL 2014), BELGRADE, SERBIA, 12-14 MAY, 2014

Investigation of the Microcantilevers by the Photoacoustic Elastic Bending Method

D. M. Todorović, V. Jović, K. T. Radulović, M. Sarajlić, D. Markushev, M. D. Rabasović

Abstract – The amplitude of the photoacoustic (PA) elastic bending signals vs. the modulation frequency of the excitation optical beam for the chip with Si cantilevers were measured and analyzed. The experimental PA elastic bending signals of the whole micromechanical structure were measured by using special constructed PA cell (the gas-microphone detection technique with transmission configuration). The PA spectra were measured in a frequency range from 20 to 20000 Hz. The signal in the PA cell without optical excitation (noise) was also measured and analyzed. Experimental results show that the PA measuring system (PA cell width electret's microphone and lock-in amplifier) has signal-noise ratio S/N ~ 30000 at 100 Hz; ~ 3000 at 1000 Hz; ~ 5 at 10000 Hz. The correction of the measured signal, in order to remove the coherent electronic noise as a systematic error, was made. The experimental PA elastic bending signals of the cantilever were compared with the experimental PA elastic bending signals of the Si square membranes. These results showed that the PA elastic bending method is convenient for investigation the characteristics of micromechanical structures as microcantilevers.

I. INTRODUCTION

The development of micro(nano)system technologies (surface and bulk micromachining) resulted in the production of miniature sensors, actuators, resonators and electromechanical parts [1,2,3,4]. One of main problem is the method of characterization of these microstructures.

The photoacoustic (PA) and photothermal (PT) science and technology extensively developed new methods for the investigation of micro (nano) – mechanical structures. The PA and PT effects can be important also as driven mechanisms for optically excited micromechanical structures [5].

The PA elastic bending method is based on the

optical excitation of the micromechanical structure and detection of the acoustic response (PA signal) with a very sensitive PA detection system. The basic concept and application of the PA elastic bending method are presented. The amplitude and phase of the PA elastic bending signals vs. the modulation frequency of the excitation optical beam for the cantilevers were measured and analyzed.

The PT and PA effects in micromechanical structures are based on the photogeneration of electron-hole pairs, i.e. plasma waves, generated by the absorbed intensity-modulated excitation. Plasma waves contribute to the generation of periodic heat. The plasma and thermal waves produce periodic elastic deformation in the sample – the plasmaelastic (PE) and thermoelastic (TE) displacements. On the other hand, PE and TE mechanisms are main mechanisms of elastic displacement generation in optically driven micromechanical structures, i.e. for optically driven structures for sensors and actuators.

The analysis of the elastic bending, i.e. thermoelastic (TE) and plasmaelastic (PE) effects in micromechanical structures consists in modeling a complex system of the plasma, thermal and elastic wave equations [ 6 ]. In previously published papers, Todorović et al. [7, 8, 9, 10], the plasma thermal and TE and PE effects, i.e. the plasma, thermal and elastic fields photogenerated by a laser beam in cantilevers were theoretically and experimentally investigated.

In this work, the experimental PA elastic bending signals of the whole micromechanical structure were measured by using special constructed PA cell (the gas-microphone detection technique with transmission configuration). The PA amplitude spectra were measured, as a function of the modulation frequency in a frequency range from 20 to 20000 Hz, for Si chip with cantilever. The signal-noise ratio (S/N) of the PA measuring system was analyzed. The experimental PA elastic bending signals of the cantilever are compared with the experimental signals of the Si square membranes.

Dragan M. Todorović, is with the Institute for Multidisciplinary Research, University of Belgrade, PO.Box 33, 11030 Belgrade, Serbia , E-mail: dmtodor@afrodita.rcub.bg.ac.rs Vesna Jović, Katarina T. Radulović and M. Sarajlić, are with Institute for chemistry, technology and metallurgy, Njegoseva 12, 11000 Belgrade, Serbia. Dragan D. Markushev and Mihailo D. Rabasović are with Institute for Physics, University of Belgrade, Prigrevica 118, 11080 Belgrade-Zemun, Serbia

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II. EXPERIMENTAL RESULTS

A. Experimental Setup The PA spectra were measured by using the PA

elastic bending method. The optically generated elastic bending in the sample is detected over the PA effect. The experimental PA elastic bending signals of the whole micromechanical structure (Si chip with rectangular cantilever mounted directly to the microphone) were measured by using special constructed PA cell [11] (the gas-microphone detection technique with transmission configuration, Fig. 1)

The PA cell uses a miniature electrets microphone as an acoustic detector; the sample was mounted directly onto a front surface of microphone, which usually has a circular hole as the sound inlet. It uses the internal microphone air chamber, adjacent to the membrane, as a conventional measuring gas chamber of PA cell. The construction of the PA cell was optimized to get maximum acoustic protection

from the surroundings, a good signal/noise ratio in the frequency range between 20 and 20000 Hz. The samples were excited by electronically modulated LED (the wavelength ~640 nm). Fig. 1 shows the PA setup and Si chip with rectangular cantilever.

B. Si Chip with Cantilever

Samples were prepared from 3 inch, 390 m thick,

double side polished, 3-5 cm n-type (100) Si wafers. Masking material was thermally grown SiO2. SiO2 is grown at 1100 oC from oxygen saturated with water vapor. Oxide thickness is about 1 m. Etch square windows (3200 x 3200 m2) oriented in 110 direction in masking materials were defined through lithography on one wafer side. Si cantilevers were fabricated by wet anisotropic bulk micromachining process. Potassium hydroxide (KOH) solution in water is used as enchant of Si. The micromachining is carried out at 80 oC using 30 wt% KOH solutions. Cantilever thickness is function of etching time. After cantilever fabrication, and dicing single elements, remaining masking material was completely removed.

C. Experimental PA elastic Bending Spectra The PA elastic bending spectra were measured and

analyzed vs the frequency of modulation of the optical excitation. The experimental PA amplitude and phase spectra were measured as a function of the modulation frequency in a frequency range from 20 to 20000 Hz for Si chip with rectangular cantilevers. All experimental amplitude PA elastic bending spectra used in this paper are the mean values of at least five measurements at the same excitation and detection position. Typical experimental amplitude PA elastic bending spectra for Si chip with rectangular cantilevers (Si chip, frame 5 x 5 mm, rectangular cantilever 2.5 x 2.0 mm, thickness 100 µm) is given in Fig.2. Fig.2 shows also the experimental signal without the optical excitation (noise).

III. ANALYSIS AND DISCUSSION

A. PA Signal –Noise Ratio Experimental results show that the PA measuring

system (PA cell width electret microphone and lock-in amplifier) has S/N ~ 30000 at 100 Hz; ~ 3000 at 1000 Hz; ~ 5 at 10000 Hz. It is clear from that analyze that for frequency above 10000 Hz, the PA signal is small and comparable with the noise (coherent electronic noise increase with increasing the frequency; the sensitivity of the acoustic detector, i.e. the electrets microphone decrease in this frequency range). It is possible to see that for the

optical excitation

Si chip

microphone

sample holder

( a )

400

100

Si

Epo-Tek H77

Pyrex glass

all dimensions are in micrometers

5005002000

1000 1000

2500

700

2142

( b ) Fig. 1 Photoacoustic elastic vibration method: ( a ) cross-section of the PA cell with the sample (Si chip 5 x 5 mm with glass cover); ( b ) cross-section and dimension of the Si chip with rectangular cantilever and the glass cover.

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102

103

10410

-7

10-6

10-5

10-4

10-3

10-2

10-1

frequency [ Hz ]

PA

am

plitu

de

[ a.u

. ]

Si chip CL 100um : ( * ) signal (S1); ( . ) noise (S2 + S3)

Fig.2 Typical experimental PA amplitude elastic bending spectra of the Si rectangular cantilever (Si chip, <100>, frame 5 x 5 mm, cantilever 2.5 x 2.0 mm, 100 μm thick): ( o ) with optical excitation (signal); ( · ) without the optical excitation (noise).

sample with the thickness of 100 μm, the noise significantly changes the PA amplitude above the frequencies ~10 kHz. For this reason it is necessary to make a correction of the measured signal, in order to remove the coherent electronic noise as a as a systematic error.

B. PA Signal Frequency Correction In the low frequency range the experimental PA

signal deviates from the theoretical. This is the consequence of the input impedance of the lock-in amplifier (non adapted electret's microphone output impedance to the input of the lock-in amplifier). In the high frequency range the experimental PA signal also deviates significantly from the theoretical. This is the consequence of the acoustic characteristic of the PA cell. To solve this problem it is necessary to correct the experimental PA signal. Using the measured signals from the PA cell (with and without optical excitation) can be made corrections PA signal and remove these systematic errors in amplitude and phase at low and high frequencies. Correction procedure of the experimental signal is given in previously published work Todorovic et al [12].

The low frequency correction can be given as:

,)1()1(

)(2

mi

miLF

jjA

(1)

where τi = Ri Ci is the time constant of the measuring instrument (lock-in amplifier) and τm is the time constant of the microphone. The time constant of the lock-in amplifier is known from the instrument specification, i.e. τi = 400 μs (Ri = 10 MΩ and Ci = 40 pF), while the τm = 16 ms is obtained from the fitting experimental PA signal with the theoretical one. In the high frequency range the experimental PA signal also deviates significantly from the theoretical. This is the consequence of the acoustic characteristic of the PA cell and sample mounting on the front to the microphone (the acoustic measuring volume is the sum of the acoustic volume below the sample and microphone volume connected with a short pipe – microphone inlet). This complex acoustic measuring volume can be simulated as a Helmholtz resonator, i.e. as a damped harmonic oscillator. The high frequency correction of the experimental PA signal can be given as:

,)(

)( 2

22

c

ccHF jA

(2)

where ωc = 2πf c is the characteristic frequency of the PA cell and δc is the damping factor. The characteristic frequency f c was obtained from the experimental PA amplitude, while the δc is obtained from the fitting experimental PA signal with the theoretical one (f c = 8.20 kHz and δc = 1.4·104 ).

Fig. 3 shows corrected amplitude PA signals vs. modulation frequency for the 100 um thick cantilever (Si chip, <100>, frame 5 x 5 mm, cantilever 2.5 x 2 mm).

C. PA Signal of the Cantilever and Membrane

To see the effect of elastic vibrations, ie TE and PE

effects on the PA signal, in addition to measurements of the cantilevers were performed measurements on thin Si membranes, which are the same thickness and similar sized area. The PA experimental results in Fig. 3 for rectangular cantilever and square membrane (Si chip, <100>, frame 5 x 5 mm, membrane 2.7 x 2.7 mm) shows the significant difference between the PA amplitude curves for cantilever and membrane.

The experimental PA amplitude curves show that the curve slopes change approximately with modulating frequency of the optical excitation f = ω/2π, as ~ f -S, where s is the curve slope. For example, the analyse of the corrected experimental amplitude spectra gives that for Si membrane the curve slope at f < 5 kHz is s(MEM) ≈ 1.50, while for cantilever the curve slope is s(CL) ≈ 1.50 at f < 0.9 kHz and it changes to s(CL) ≈ 1.25 at f > 0.9 kHz. These differences are the consequence of the different caracter of elastic vibrations of the cantilever and square membrane, i.e. the consequence of the different TE and PE effects. In the low frequency range, the experimental amplitude spectra have f -1.50 behavior, typical for the TD

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101

102

103

104

10-7

10-6

10-5

10-4

10-3

10-2

10-1

frequency [ Hz ]

PA

am

plitu

de

[ a.u

. ]

Si chip, 100 um: ( . ) MEM; ( o ) CL

Fig.3 Corrected experimental PA amplitude elastic bending spectra of the Si chip with: ( o ) rectangular cantilever and ( · ) square membrane. The cantilever and membrane have the same thickness (100 μm) and similar surfaces.

component of PA signal in the case of the thermally thick samples (where the sample thickness is much smaller than the thermal diffusion length). On the other side, the TE and PE effects are more significant for cantilever than for membrane (at the higher frequencies f >1 kHz).

IV. CONCLUSION The mechanical vibration characteristics of the Si

chip with rectangular cantilevers were analyzed. The amplitude of the PA elastic bending signals vs. the modulation frequency of the excitation optical beam for the chip with Si cantilevers were measured and analyzed. The

PA spectra were measured in a frequency range from 20 to 20000 Hz. The signal in the PA cell without optical excitation (noise) was also measured and analyzed. Experimental results show that the PA measuring system PA cell width electret's microphone and lock-in amplifier) has signal-noise ratio S/N ~ 30000 at 100 Hz; ~ 3000 at 1000 Hz; ~ 5 at 10000 Hz. The correction of the measured signal, in order to remove the coherent electronic noise as a systematic error, was made. The experimental PA elastic bending signals of the cantilever were compared with the experimental PA elastic bending signals of the Si square membranes. These results showed that the PA elastic bending method is convenient for investigation the characteristics of micromechanical structures as cantilevers.

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