Piezoelectric sensors used for the detection of chemical
agents and for electronic nose instruments are based on BAW and SAW quartz
resonators. They are also useful in the detection of biological agents, and
can be specific, particularly if the sensitive surface is activated with
the right antigen. The MEMS resonators are shaped as a silicon bar of
nanometric dimensions incased (fixed) at both ends, subject to bending
strain. They are best driven by an AC current flowing in a very thin
straight wire attached along the bar, in the presence of a strong constant
magnetic field, perpendicular to it.
The BAW resonators are used for instance in the "quartz
crystal microbalance" (QCM). This is usually a small polymer-coated
resonating quartz disk, with smaller diameter metal electrodes on each side
and with quality factor Q. The resonance frequency is usually in the 50 MHz
range. Absorption of gas molecules with mass dm
on the surface of the polymer coating gets detected by a reduction y=dn/n=-kdm/m of the
resonance frequency of the quartz disk, subject to frequency fluctuations.
The quantum 1/f limit of detection is given by
k2Sdm/m(f)=Sy(f), with Sy(f) = b'V/fQ4, for V<<e, and S(f) = b'e2/fVQ4, for V>>e,
where e is the phonon
coherence volume, first introduced by T. Parker et. al. as a noise
coherence volume. To optimize the device we must avoid closeness of V
with e which corresponds to the maximum error
and minimal sensitivity situation. Differential measurements that
include a reference resonator without polymer coating can effectively
eliminate temperature fluctuations, power supply instability, etc. Adsorbed
masses below the pg=10-12g range can be detected. With <w>=108/s being the average circular frequency of a
thermal phonon interacting with phonons in the main resonator mode, with
n=kT/<w> being the average number of
phonons in that typical thermal phonon mode, and with T=300K, we obtain
approximately the quantum 1/f noise coefficient
1022(1/137)(10-27108)2/12kTp10-27.9.1020 Å = 1.
For V<e, his is in good
agreement with the known data for quartz resonators of very high Q as
experimental results obtained by Ferre-Pikal et al., T. Parker et al., J.R.
Vig et al., as well as other research groups indicate. Here m is the
reduced mass of the elementary oscillating dipoles, N their number in the
quartz resonator volume, and g a polarization constant of the order of the
unity. The formulas given above are derived from the equation
SdG/G(f) = 4a(Dv)2/3pfe2c2.
of the conventional quantum 1/f effect applied to the
energy dissipation G of a quartz crystal. Here
DP/V is the change in the quartz polarization
rate caused by the elementary dissipative process of removing a phonon from
the main resonator mode.
Similarly, SAW resonators are used at about ten times
higher frequencies in SAW sensors that operate in the V>e regime with b=120.
The discussion is similar, but applied to the surface and to surface
Peter H. Handel
Department of Physics and Astronomy, University of Missouri
8001 Natural Bridge Rd., St. Louis, MO 63121 USA
email: firstname.lastname@example.org http://www.umsl.edu/~handel