Everything about Piezoelectric Microbalance totally explained
A
quartz crystal microbalance (QCM) measures a mass per unit area by measuring the change in
frequency of a
quartz crystal resonator. The
resonance is disturbed by the addition or removal of a small mass due to oxide growth/decay or film deposition at the surface of the acoustic resonator. The QCM can be used under vacuum, in gas
phase ("gas sensor", first use described by
[58]) and more recently in liquid environments. It is useful for monitoring the rate of deposition in
thin film deposition systems under vacuum. In liquid, it's highly effective at determining the
affinity of molecules (
proteins, in particular) to surfaces functionalized with recognition sites. Larger entities such as
viruses or
polymers are investigated, as well. Frequency measurements are easily made to high precision (discussed below); hence, it's easy to measure mass densities down to a level of below 1 μg/cm
2. In addition to measuring the frequency, the
dissipation is often measured to help analysis. The dissipation is a parameter quantifying the
damping in the system, and is related to the sample's
viscoelastic properties.
General
Quartz is one member of a family of
crystals that experience the
piezoelectric effect. The piezoelectric effect has found applications in high power sources, sensors, actuators, frequency standards, motors, etc., and the relationship between applied
voltage and mechanical deformation is well known; this allows probing an acoustic resonance by electrical means. Applying alternating current to the quartz crystal will induce oscillations. With an alternating current between the electrodes of a properly cut crystal, a standing
shear wave is generated. The
Q factor, which is the ratio of frequency and
bandwidth, can be as high 10
6. Such a narrow resonance leads to highly stable oscillators and a high accuracy in the determination of the resonance frequency. The QCM exploits this ease and precision for sensing. Common equipment allows resolution down to 1 Hz on crystals with a fundamental
resonant frequency in the 4 – 6 MHz range. A typical setup for the QCM contains water cooling tubes, the retaining unit, frequency sensing equipment through a microdot feed-through, an oscillation source, and a measurement and recording device.
The frequency of oscillation of the quartz crystal is partially dependent on the thickness of the crystal. During normal operation, all the other influencing variables remain constant; thus a change in thickness correlates directly to a change in frequency. As mass is deposited on the surface of the crystal, the thickness increases; consequently the frequency of oscillation decreases from the initial value. With some simplifying assumptions, this frequency change can be quantified and correlated precisely to the mass change using
Sauerbrey's equation.
[1]
Other techniques for measuring the properties of thin films include
Ellipsometry,
Surface Plasmon Resonance (SPR)
Spectroscopy, and
Dual Polarisation Interferometry.
Gravimetric and Non-Gravimetric QCM
The classical sensing application of quartz crystal resonators is microgravimetry.
[2,3, 4, 5] Many commercial instruments, some of which are called
thickness monitors, are available. These devices exploit the Sauerbrey relation
[1]. For thin films, the resonance frequency is – by-and-large – inversely proportional to the total thickness of the plate. The latter increases when a film is deposited onto the crystal surface.
Monolayer sensitivity is easily reached. However, when the film thickness increases, viscoelastic effects come into play.
[6] In the late 80’s, it was recognized that the QCM can also be operated in liquids, if proper measures are taken to overcome the consequences of the large damping.
[7,8] Again, viscoelastic effects contribute strongly to the resonance properties.
Today, microweighing is one of several uses of the QCM. Measurements of
viscosity and more general, viscoelastic properties, are of much importance as well. The “non-gravimetric” QCM is by no means an alternative to the conventional QCM. Many researchers, who use quartz resonators for purposes other than gravimetry, have continued to call the quartz crystal resonator “QCM”. Actually, the term "balance" makes sense even for non-gravimetric applications if it's understood in the sense of a
force balance. At resonance, the force exerted upon the crystal by the sample is balanced by a force originating from the shear gradient inside the crystal. This is the essence of the small-load approximation.
Crystalline α–quartz is by far the most important material for thickness-shear resonators.
Langasite (La
3Ga
5SiO
14, “LGS”) and
gallium-orthophosphate (GaPO
4) are investigated as alternatives to quartz, mainly (but not only) for use at high temperatures.
[9,10] Such devices are also called “QCM”, even though they're not made out of quartz (and may or may not be used for gravimetry).
Surface Acoustic Wave Based-Sensors
The QCM is a member of a wider class of sensing instruments based on acoustic waves at surfaces. Instruments sharing similar principles of operation are shear horizontal
surface acoustic wave (SH-SAW) devices,
[11,12]
Love-wave devices
[13], and
torsional resonators
[14,15]. Surface acoustic wave-based devices make use of the fact that the reflectivity of an acoustic wave at the crystal surface depends on the
impedance (the stress-to-speed ratio) of the adjacent medium. (Some acoustic sensors for temperature or pressure make use of the fact that the speed of sound inside the crystal depends on temperature, pressure, or bending. These sensors don't exploit surface effects.) In the context of surface-acoustic wave based sensing, the QCM is also termed “bulk acoustic wave resonator (BAW-resonator)” or “thickness-shear resonator”. The displacement pattern of an unloaded BAW resonator is a standing shear wave with
anti-nodes at the crystal surface. This is makes the analysis particularly easy and transparent.
Instrumental
Resonator Crystals
When the QCM was first developed, natural quartz was harvested, selected for its quality and then cut in the
lab. However, most of today’s crystals are grown in the lab using
seed crystals. The seed crystals serve as an anchoring point for crystal growth; encouraging growth in two directions and limiting growth in another. The crystals, AT or SC (discussed below) used in most applications operate in the thickness shear mode at a frequency in the 1-30 MHz range.
[18]
Electromechanical Coupling
The QCM consists of a thin piezoelectric plate with electrodes evaporated onto both sides. Due to the piezo-effect, an AC voltage across the electrodes induces a shear deformation and vice versa. The electromechanical coupling provides a simple way to detect an acoustic resonance by electrical means. Otherwise, it's of minor importance. However, electromechanical coupling can have a slight influence on the resonance frequency via piezoelectric stiffening. This effect can be used for sensing,
[20] but is usually avoided. It is essential to have the electric and
dielectric boundary conditions well under control. Grounding the front electrode (the electrode in contact with the sample) is one option. A π-network sometimes is employed for the same reason.
[21] A π-network is an arrangement of
resistors, which almost
short-circuit the two electrodes. This makes the device less susceptible to electrical perturbations.
Shear Waves Decay in Liquids and Gases
Most acoustic-wave-based sensors employ shear (transverse) waves. Shear waves decay rapidly in liquid and gaseous environments.
Compressional (longitudinal) waves would be radiated into the bulk and potentially be reflected back to the crystal from the opposing cell wall.
[22,23] Such reflections are avoided with transverse waves. The range of penetration of a 5 MHz-shear wave in water is 250 nm. This finite penetration depth renders the QCM surface-specific. Also, liquids and gases have a rather small shear-acoustic impedance and therefore only weakly damp the oscillation. The exceptionally high Q-factors of acoustic resonators are linked to their weak coupling to the environment.
Modes of Operation
Economic ways of driving a QCM make use of oscillator circuits.
[24,25] Oscillator circuits are also widely employed in time and frequency control applications, where the oscillator serves as a clock. Other modes of operation are impedance analysis
[26] and ring-down.
[27,28] In impedance analysis, the
electric conductance as a function of driving frequency is determined by means of a
network analyzer. By fitting a resonance curve to the conductance curve, one obtains the frequency and bandwidth of the resonance as fit parameters. In ring-down, one measures the voltage between the electrodes after the exciting voltage has suddenly been turned off. The resonator emits a decaying
sine wave, where the resonance parameters are extracted from the period of oscillation and the decay rate.
Energy Trapping
The electrodes at the front and the back of the crystal usually are key-hole shaped, thereby making the resonator thicker in the center than at the rim. This confines the displacement field to the center of the crystal by a mechanism called energy trapping.
[29] The crystal turns into an acoustic lens and the wave is focused to the center of the crystal. Energy trapping is necessary in order to be able to mount the crystal at the edge without excessive damping. Energy trapping slightly distorts the otherwise planar wave fronts. The deviation from the plane thickness-shear mode entails flexural contribution to the displacement pattern. Flexural waves emit compressional waves into the adjacent medium, which is a problem when operating the crystal in a liquid environment.
Overtones
Planar resonators can be operated at a number of
overtones, typically indexed by the number of nodal planes parallel to the crystal surfaces. Only odd
harmonics can be excited electrically because only these induce charges of opposite sign at the two crystal surfaces. Overtones are to be distinguished from anharmonic side bands (spurious modes), which have nodal planes perpendicular to the plane of the resonator. The best agreement between theory and experiment is reached with planar, optically polished crystals for overtone orders between
n = 5 and
n = 13. On low harmonics, energy trapping is insufficient, while on high harmonics, anharmonic side bands interfere with the main resonance.
[30]
Amplitude of Motion
The
amplitude of lateral displacement rarely exceeds a nanometer. More specifically one has
The QCM allows for non-destructive testing of the shear stiffness of multi-asperity contacts.
Further Information
Get more info on 'Piezoelectric Microbalance'.
|
External Link Exchanges
Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:
<a href="http://quartz_crystal_microbalance.totallyexplained.com">Quartz crystal microbalance Totally Explained</a>
Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned. |
