Improved quartz crystal microbalance technique

Abstract

The importance of using the most pertinent mathematical description of the mass load versus frequency relation for quartz crystal thin-film thickness monitors is reviewed. The different usable crystal load ranges of the so-called frequency- and period-measurement techniques in comparison with the Z-Match technique are calculated for most of the commonly used deposition materials. A new thin-film thickness monitoring procedure is described, which takes the influence of the acoustic film properties on the mass load versus frequency slope into consideration without need for the explicit knowledge of the acoustic impedance ratio z of the deposited film and the quartz crystal. It is shown how the effective z value in the composite resonator built by the quartz crystal and the deposited foreign layer can be derived from a measurement of a quasiharmonic overtone resonance frequency in addition to the commonly practiced exclusive measurement of the fundamental resonance frequency. The presently established relation between the mass load or the deposited film thickness and the corresponding resonance frequency of the loaded crystal is enhanced by a more rigorous one-dimensional composite resonator description. The introduced so-called series resonance relation is of significance for the accurate determination of the specific acoustic impedance ratio z of the deposited film and the crystal. Furthermore, the deviations of the frequency spectra of plano-convex shaped crystals from that of the one-dimensional (infinite plate) geometry are investigated and taken into account. The achieved accuracy in the z determination from the first and third quasiharmonic frequencies justifies the applicability of the two-frequency or auto slope accommodation technique introduced in this paper.

Thermophysical Properties of Penetrants in Polymers via a Piezoelectric Quartz Crystal Microbalance

“…For small mass charges, the decrease in a thickness shear mode frequency of a crystal upon which a thin film is deposited is linearly proportional to the deposited mass. The linear mass-frequency relation is valid upto a mass load of 2% (Benes, 1984). In addition, the linear mass-frequency relation was found to be valid until the frequency decrease due to loading is approximately 2 % of the unloaded frequency (Lu, 1975).…”

“…In the equivalent circuit, the resistance increases as more material is deposited onto the crystal. The resistance increase is due to the increase in the acoustic losses in the coated material (Benes, 1984).…”

“…The latest crystal thickness monitors based on the Equations (34)- (38) are called Z-match technique devices. The only drawback of these thickness monitors is the knowledge of acoustic impedance ratio and the necessity of manually keying a Z value for every deposited material (Benes, 1984).…”

“…The basic assumption made by Stockbridge is that the amount of potential energy stored in the deposited foreign layer during oscillation is negligible. This restricts the use of linear mass-frequency relationship to a small film thicknesses with negligible shear deformation (Benes, 1984). Equation 28 has been tested by Sauerbrey by evaporating thin metal films onto quartz crystals and monitoring the change in frequency (Hlavay and Guilbault, 1977).…”

Online Drift Compensation for Chemical Sensors Using Estimation Theory

“…The polymer solutions were spin-coated on the device surface (over the IDTs and the delay path) and allowed to dry in a desiccator (room temperature of 22 C) for at least 12 h to obtain an approximate thickness around 1 m. Thickness calibration was performed using thickness-shear mode (TSM) resonators in conjunction with the Sauerbrey equation [17]. However, it is noted that the calibration results only in an approximate thickness, as Sauerbrey's equation is not valid for viscoelastic layers [18], [19].…”