Diamond – Application to piezoelectric bimorph cantilever sensors

phys. stat. sol. (a) 203, No. 12, 3185–3190 (2006) / DOI 10.1002/pssa.200671109

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Original

Paper

Diamond – Application to piezoelectric bimorph

cantilever sensors

V. Mortet*, 1, 2, K. Haenen1, 2, J. Potmesil 3, M. Vanecek3, and M. D’Olieslaeger1, 2

1 Hasselt University, Institute for Materials Research (IMO), Wetenschapspark 1,

3590 Diepenbeek, Belgium 2 IMEC vzw, Division IMOMEC, Wetenschapspark 1, 3590 Diepenbeek, Belgium 3 Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnicka 10, 16253 Prague 6,

Czech Republic

Received 28 February 2006, revised 19 June 2006, accepted 23 June 2006

Published online 29 August 2006

PACS 43.58.+z, 68.37.Ps

Micro-cantilevers are excellent tools to measure tiny forces (from 1 nN up to 10 µN) as shown by the de-

velopment of atomic force microscopy (AFM) techniques. That is the reason why micro-cantilevers are

also the most sensitive acoustic sensors. For instance, one can use the variation of the cantilever’s reso-

nant frequency to measure mass loading. In this work, we will show first why diamond is the most suit-

able material for a special type of cantilever sensors: piezoelectric bimorph cantilever sensors. In contrast

to other cantilevers, it is possible to actuate piezoelectric bimorph cantilevers and to detect their resonance

frequencies simultaneously. Then, we present one application of this type of cantilever: a diamond/AlN

cantilever used as a high pressure sensor (up to 7 ar). The sensor operates by monitoring the frequency

shift of the first resonant mode (f1 ~ 36.5 kHz). We have measured a sensitivity of 0.155 Hz/mbar in pure

nitrogen.

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

Atomic force microscopy (AFM) is one of the main application domains of microcantilevers. They are

use to transduce tiny forces that interact with a sharp tip at the cantilevers’ free end. Most microcantile-

vers are made of silicon. Due to its extreme hardness and its low wear coefficient, diamond has been

already used as a protection layer for silicon tips [1] as well as tips [2]. Monolithic diamond cantilevers

for AFM have also been made [3]. While diamond processes high fracture toughness, the high Young’s

modulus of diamond gives to diamond cantilevers a higher spring force constant (k), ~10 times higher

than silicon cantilevers. For a rectangular cantilever geometry, 3 34k E t w L= ◊ ◊ ◊ , where E is Young’s

Modulus, t the thickness, w the width and L the length of the cantilever [4]. Diamond cantilevers have

also slightly higher resonant frequencies ( fi) than silicon cantilever. The resonant frequencies of a canti-

lever are proportional to E ρ , where ρ is the density [5]. Diamond and silicon properties for AFM

cantilever applications are reported on Table 1 for comparison. Microcantilevers can also be used as

sensors with extreme sensitivity. In 1994, it was found for the first time that a standard AFM cantilever

could operate as a microcalorimeter with fentojoule (10 –15 J) sensitivity [7]. Microcantilevers operate by

detecting changes in the resonant response or the defection caused either by mass loading, damping or

stress. Compared to the other methods to measure the resonant frequencies of standard cantilevers [8],

* Corresponding author: e-mail: Vincent.mortet@uhasselt.be, Phone: +32 11 26 88 48, Fax: +32 11 26 88 99

3186 V. Mortet et al.: Diamond – Application to piezoelectric bimorph cantilever sensors

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-a.com

Table 1 Comparison of mechanical and electrical properties of materials used for cantilevers applica-

tions.

Si (100) diamond AlN ZnO BaTiO3 PZT4

fracture toughness [6] 1 5.3 – – – –

Young’s modulus (GPa) 130 1050 – – – –

c11 coefficient (GPa) 165.6 1079 345 210 275 139

density (g ⋅ cm–3) 2.33 3.5 3.3 5.68 5.8 7.5

normalized E ρ 1 2.26 – – – – 2

fK – – 1.03 1.71 2.63 3.47

piezoelectric bimorph cantilevers are more interesting since it is possible to actuate and to detect their

resonant frequencies electrically and simultaneously.

In this paper, we emphasize the interest of using diamond in bimorph piezoelectric cantilevers for

sensor applications, then we describe the experimental process to make a diamond/aluminium nitride

bimorph cantilever and we present the first experimental result of a pressure sensor operating at room

temperature made with a diamond/AlN cantilever.

2 Theory

A piezoelectric bimorph cantilever consists of a piezoelectric layer deposited on an elastic substrate

having its upper face coated with a metallic electrode. A second electrode is deposited on the top of the

piezoelectric thin film. Vibrations of cantilevers [9] and bimorph piezoelectric cantilevers [10] have

already been studied. The resonant frequencies of a bimorph piezoelectric cantilever are:

2

2

H

,2π

i

i

a Df

L ρ=

◊

(1)

where L is the length, D the transverse flexural rigidity, ρH the total mass per unit surface of the bimorph

and ai are the root of the equation 1+ cosh (x) ⋅ cos (x) = 0 [9]. The admittance (Y) and the electromecha-

0.0 0.2 0.4 0.6 0.8 1.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Normalized substrate thickness

For

mfa

ctor

F(a

.u.)

Normalized piezoelectic film thickness

0.250.50.7512345678910O

Ys/C

11

Ys/C

11increasing

0.00.20.40.60.81.0

Fig. 1 (online colour at: www.pss-a.com) Form factor as a function of the normalized thicknesses of the

substrate (hs/(h

s + h

c)) and the piezoelectric layer (h

c/(h

s + h

c)), the substrate Young’s modulus and elastic

constant of the piezoelectric material ratio: Ys/c

11. The symbol () corresponds to the diamond/AlN canti-

lever studied in this article.

phys. stat. sol. (a) 203, No. 12 (2006) 3187

www.pss-a.com © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Original

Paper

nical coupling coefficient (k2) can also be determined: 2

0(1 )Y j C kω= - - , where C0 is the static capaci-

tance formed by the piezoelectric material between the two electrodes. The electromechanical coupling

coefficient is 2 2

fk K F= , where F is a form factor and 2 2 E S

31 11 33( )fK e c ε= ◊ is the electromechanical cou-

pling factor of the piezoelectric material with e31 the piezoelectric coefficient at constant field, E

11c the

elastic constant, S

33ε the permittivity at constant strain. The form factor is a function of the Young’s

modulus (Ys) and the thickness (hs) of the substrate, the elastic constant ( E

11c ) and the thickness (hc) of the

piezoelectric material, and it is linear with 1/L. To optimize the electromechanical coupling coefficient

(k2), it is necessary to optimize both the electromechanical coupling coefficient of the piezoelectric mate-

rial ( 2

fK ) and the form factor. One can see that the most suitable piezoelectric material is PZT which has

a high electromechanical coupling coefficient (see Table 1). The variation of the form factor as a func-

tion of the mechanical and the geometric properties of the cantilever is represented in the Fig. 1. The

form factor has an optimal value as a function of the normalized substrate thickness (or normalized

piezoelectric layer thickness) and it increases with the ratio Ys /E

11c . In another words, the stiffer the sub-

strate, the higher the form factor and the electromechanical coupling coefficient. Thus, diamond, which

has the highest known Young’s modulus, is the most suitable material for this type of cantilever.

3 Experimental

3.1 Nanodiamond growth

Nano-crystalline diamond films were deposited on (100) silicon substrates (15 × 15 mm2) by microwave

plasma enhanced chemical vapor deposition in an Aixtron P6 deposition system. The substrates were

bias enhanced nucleated (BEN) to achieve a high nucleation density (1010 – 1011 cm–2) and to obtain

quickly a closed film. A bias voltage of –180 V with 5% of methane in hydrogen and a total pressure of

20 mbar were applied for 12 minutes during the nucleation step [11]. The diamond films were grown in

0.5% of methane in hydrogen, with a total pressure of 20–40 mbar and a microwave power of 900 Watt

for 2–3 hours. The diamond films have a thickness of ~0.6–0.7 µm, with a root mean square roughness

of 15–20 nm and the grain size is in the range of 30–100 nm.

3.2 Aluminium nitride growth

The piezoelectric aluminum nitride (AlN) films were deposited by magnetron sputtering [12]. The nitro-

gen concentration ΦN/(ΦAr + ΦN), where ΦAr and ΦN are the argon and nitrogen flow rates, were opti-

mized to minimize the stress of the AlN layers. One can observe that the stress varies, rather linearly,

from tensile to compressive as the nitrogen ratio increases and passes through zero at a nitrogen concen-

tration of 50% (see Fig. 2).

25 50 75 100

-2

-1

0

1

Str

ess

(GP

a)

N2

concentration (%)

Total gas flow: 50sccmTotal gas flow: 100sccm

Fig. 2 (online colour at: www.pss-a.com) Variation of the mechanical stress in AlN films as a function of the nitrogen concentration in the gas discharge.

3188 V. Mortet et al.: Diamond – Application to piezoelectric bimorph cantilever sensors

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-a.com

35500 36000 36500 37000 37500

82.0k

84.0k

86.0k

88.0k

90.0k

92.0k

-90

-88

-86

-84

-82

-80

Pha

sesh

ift(°

)

Impe

danc

em

odul

us(Ω

)

Frequency (Hz)

Fig. 3 (online colour at: www.pss-a.com) Variation of the impedance modulus and the phase-shift of diamond/AlN micro-cantilever as a function of the frequency at the first resonant mode. The dash line represents the static capacitance.

3.3 Diamond/AlN micro-cantilevers processing and experimental setup

Diamond/AlN micro-cantilevers have been fabricated using photolithography techniques, diamond reac-

tive ion etching in oxygen plasma and wet anisotropic etching of the silicon substrate. The cantilever that

we have made in this work is 320 µm long, 70 µm wide, its diamond layer is 0.6–0.7 µm thick, its AlN

layer is 1 µm thick and the electrodes are 100 nm thick.

To measure the pressure sensitivity, the cantilever was fixed into a gas tight enclosure and it was elec-

trically connected to an impedance analyzer (HP 4194A) with a BNC cable. The pressure in the canister

was regulated with relief valve at the gas inlet and a leaking valve at the gas outlet. The pressure was

measured with a tire manometer. In this study, the pressure has been varied from vacuum up to 7 ar.

Experiments were carried out in pure nitrogen.

4 Results and discussion

First, we have measured the different resonant frequencies of the cantilever under vacuum, i.e. without

gas damping. Figure 3 shows the impedance characteristic plot of the diamond/AlN cantilever at the first

resonant mode. The impedance modulus decreases to a minimum, crosses the impedance curve of the

static capacitance, increases to a maximum and finally decreases and tends to the static capacitance im-

pedance curve. The mechanical resonance frequency of the cantilever is located at the maximum of the

phase-shift and at the crossing with the static capacitive impedance curve. The experimental resonant

Table 2 Comparison of experimental (under vacuum) and theoretical resonant frequencies of the dia-mond /AlN micro-cantilever.

mode experimental

frequency (kHz)

theoretical

frequency (kHz)

1 1,136.6 1,133.4

2 1,216 1,209.3

3 1,588 1,586.0

4 1,109 1,149

5 1,643 1,899

6 2,831 2,836

phys. stat. sol. (a) 203, No. 12 (2006) 3189

www.pss-a.com © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Original

Paper

34500 35000 35500 36000 36500 3700087.5k

90.0k

92.5k

95.0k

Impe

danc

em

oulu

s( Ω

)

Frequency (Hz)

1.5 bar2.0 bar2.5 bar3.0 bar3.5 bar4.0 bar4.5 bar5.0 bar5.5 bar6.0 bar6.5 bar7.0 bar

(a)

34000 34500 35000 35500 36000 36500 37000

-90.0

-89.8

-89.6

-89.4

-89.2

-89.0

-88.8

-88.6

-88.4

Pha

sesh

ift(°

)

Frequency (Hz)

1.5 bar2.0 bar2.5 bar3.0 bar3.5 bar4.0 bar4.5 bar5.0 bar5.5 bar6.0 bar6.5 bar7.0 bar

(b)

Fig. 4 (online colour at: www.pss-a.com) Variation of the impedance modulus (a) and the phase-shift (b) of dia-mond/AlN micro-cantilever with frequency at the first resonant mode as a function of nitrogen pressure.

frequencies values match quite well the theoretical values obtained using the diamond and AlN proper-

ties reported in Table 2.

The variation of impedance and the resonant frequency of the first resonant mode as a function of the

pressure at room temperature are represented on Figs. 4 and 5, respectively. One can see that the imped-

ance modulus and the phase shift amplitude decrease, as well as the resonant frequency, with increasing

pressure. The variation of the resonant frequency exhibits a linear behaviour as function of the pressure.

The variations of the impedance and the resonance frequency with nitrogen pressure are due to the varia-

tion of the drag force that the gas applied onto the oscillating cantilever and which is a function of the

viscosity and density of the gas [13]. The sensitivity of the cantilever in nitrogen is 0.155 Hz/mbar. Thus,

assuming that the resonant frequency can be measured with 6 digits accuracy, this pressure sensor has a

sensitivity of ~1 mbar.

5 Conclusion

We have shown that diamond is the optimal material to obtain high electromechanical coupling coeffi-

cient when it is used to make piezoelectric bimorph micro-cantilever sensors. We have grown thin

nano-diamond layers and low stress AlN films to make a diamond/AlN micro-cantilever. The resonant

frequencies of this cantilever has been measured in vacuum. Their values are in good agreement with

theoretical ones. We have also measured the variation of the first resonant frequency with nitrogen pres-

1 2 3 4 5 6 7

35200

35400

35600

35800

36000

36200

0.155 Hz/mbar

Res

onan

tfre

quen

cy(H

z)

Pressure (bar)

Fig. 5 Variation of first resonant frequency of diamond/AlN micro-cantilever as a function of nitrogen pressure.

3190 V. Mortet et al.: Diamond – Application to piezoelectric bimorph cantilever sensors

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-a.com

sure at room temperature. The resonant frequency varies linearly with the pressure with a sensitivity of

0.155 Hz/mbar. These results are preliminary and further works have to be carried out, such as the meas-

urement of the temperature sensitivity and the gas sensitivity.

Acknowledgements This work has been supported by the IWT-SBO project No. 030219 “CVD Diamond, a novel multifunctional material for high temperature electronics, high power/high frequency electronics and bioelectronics”, the projects LC 510 and GACR 202/05/2233. KH is a Postdoctoral Fellow of the Research Foundation – Flanders (FWO-Vlaanderen).

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