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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: [email protected], 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).
References
[1] E. I. Givargizov, A. N. Stepanova, E. S. Mashkova, V. A. Molchanov, F. Shi, P. Hudek, and I. W. Rangelow, Microelectron. Eng. 41/42, 499 (1998).
[2] D. Álvarez, M. Fouchier, J. Kretz, J. Hartwich, S. Schoemann, and W. Vandervorst, Microelectron. Eng. 73/74, 910 (2004).
[3] W. Kulisch, A. Malave, G. Lippold, W. Scholz, C. Mihalcea, and E. Oesterschulze, Diam. Relat. Mater. 6, 906 (1997).
[4] http://www.mobot.org/jwcross/spm/spring-constant.htm. [5] P. Gluche, M. Adamschik, A. Vescan, W. Ebert, F. Szücs, H. J. Fecht, A. Flöter, R. Zachai, and E. Kohn,
Diam. Relat. Mater. 7, 779 (1998). [6] A. R. Krauss, O. Auciello, D. M. Gruen, A. Jayatissa, A. Sumant, J. Tucek, D. C. Mancini, N. Moldovan,
A. Erdemir, D. Ersoy, M. N. Gardos, H. G. Busmann, E. M. Meyer, and M. Q. Ding, Diam. Relat. Mater. 10, 2001 (1952).
[7] T. Thundat, R. J. Warmack, G. Y. Chen, and D. P. Allison, Appl. Phys. Lett. 64, 2894 (1994). [8] R. Raiteri, M. Grattarola, and R. Beger, Mater. Today 5, 22–29 (2002). [9] L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd ed., Vol. 7 (Butterworth-Heinemann, Oxford, 1986). [10] M. Brissaud, S. Ledren, and P. Gonnard, J. Micromech. Microeng. 13, 832 (2003). [11] V. Mortet, J. D’Haen, J. Potmesil, R. Kravets, I. Drbohlav, V. Vorlicek, J. Rosa, and M. Vanecek, Diam. Relat.
Mater. 14, 393 (2005). [12] V. Mortet, M. Nesladek, J. D’Haen, G. Vanhoyland, O. Elmazria, M. B. Assouar, P. Alnot, and M. D’Olieslae-
ger, phys. stat. sol. (a) 193, 482 (2002). [13] G. Y. Chen, R. J. Warmack, T. Thundat, and D. P. Allison, Rev. Sci. Instrum. 65, 2532 (1994).