A quartz crystal microbalance (QCM), also known as quartz microbalance (QMB) and sometimes also as quartz crystal nanobalance (QCN), measures a mass variation 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 King) 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 is 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. QCM has also been used to investigate interactions between biomolecules. Frequency measurements are easily made to high precision (discussed below); hence, it is easy to measure mass densities down to a level of below 1 μg/cm2. In addition to measuring the frequency, the dissipation factor (equivalent to the resonance bandwidth) is often measured to help analysis. The dissipation factor is the inverse quality factor of the resonance, Q−1 = w/fr (see below); it quantifies 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 as 106. 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 the Sauerbrey equation. (NB. This was partially presented at Physikertagung in Heidelberg in October 1957.) Other techniques for measuring the properties of thin films include ellipsometry, surface plasmon resonance (SPR) spectroscopy, Multi-Parametric Surface Plasmon Resonance and dual polarisation interferometry.
Gravimetric and non-gravimetric QCM The classical sensing application of quartz crystal resonators is microgravimetry. Many commercial instruments, some of which are called thickness monitors, are available. These devices exploit the Sauerbrey relation. For thin films, the resonance frequency is usually 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. In the late 1980s, 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. 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 is 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.
The QCM measures inertial mass, and therefore by operating at a high resonant frequency it can be made very sensitive to small changes in that inertia as material is added to (or removed from) its surface. The sensitivity of gravitational mass measurements is, by comparison, limited by the Earth's gravitational field strength. We normally think of a balance as a way of measuring (or comparing) gravitational mass, as measured by the force that the earth exerts on the body being weighed. A few experiments have demonstrated a direct link between QCM and the SI system by comparing traceable (gravitational mass) weighings with QCM measurements.
Crystalline α–quartz is by far the most important material for thickness-shear resonators. Langasite (La3Ga5SiO14, "LGS") and gallium-orthophosphate (GaPO4) are investigated as alternatives to quartz, mainly (but not only) for use at high temperatures. Such devices are also called "QCM", even though they are 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, Love-wave devices and torsional resonators. 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 do not 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 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 using seed crystals. A seed crystal serves as an anchoring point and template for crystal growth. Grown crystals are subsequently cut and polished into hair-thin discs which support thickness shear resonance in the 1-30 MHz range. The "AT" or "SC" oriented cuts (discussed below) are widely used in applications.
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 is 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, 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.IEC standard 60444-1 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. 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. 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, QCM-I, and ring-down, QCM-D. 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 To avoid dissipation of vibration energy (damping the oscillation) by the crystal holder, which touches the crystal at the rim, the vibration should be confined to the center of the crystal platelet. This is known as energy trapping.
For crystals with high frequencies (10 MHz and higher), 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. The mass of the electrodes confines the displacement field to the center of the crystal disk. QCM crystals with vibration frequencies around 5 or 6 MHz usually have a planoconvex shape; at the rim the crystal is too thin for a standing wave with the resonance frequency. Thus, in both cases the thickness-shear vibration amplitude is greatest at the center of the disk. This means that the mass-sensitivity is peaked at the center also, with this sensitivity declining smoothly to zero towards the rim (For high-frequency crystals, the amplitude vanishes already somewhat outside the perimeter of the smallest electrode.) The mass-sensitivity is therefore very non-uniform across the crystal surface, and this non-uniformity is a function of the mass-distribution of the metal electrodes (or in the case of non-planar resonators, the quartz crystal thickness itself).
Energy trapping slightly distorts the otherwise planar wave fronts. The deviation from the plane thickness-shear mode entails flexural contribution to the displacement pattern. If the crystal is not operated in vacuum, flexural waves emit compressional waves into the adjacent medium, which is a problem when operating the crystal in a liquid environment. Standing compressional waves form in the liquid between the crystals and the container walls (or the liquid surface); these waves modify both the frequency and the damping of the crystal resonator.
Overtones