The use of piezoelectric quartz plates for the weighing of thin layers and for micro-weighing is discussed. When a foreign layer is deposited on a quartz plate excited to its free oscillation frequency, the plate's frequency changes due to the increased oscillating mass. Since the frequency change of a quartz can be measured very precisely, this leads to a highly sensitive method for weighing thin layers. The mass coverage of the foreign layer and the frequency change are proportional. The proportionality constant can be calculated from the quartz's natural frequency, eliminating the need for empirical calibration in layer weighing.
The accuracy of the layer weighing method is mainly limited by the temperature dependence of the quartz's natural frequency. At a temperature fluctuation of 1°C, the accuracy is approximately ±4×10⁻⁹ g·cm⁻², corresponding to an average thickness of 0.4 Å at a density of 1 g·cm⁻³. This method was also used for direct weighing of a mass (micro-weighing), achieving an accuracy of 10⁻¹⁰ g.
Most investigations of thin layers require the determination of the layer thickness or an equivalent parameter. Weighing is one method for measuring the thickness of thin layers. The layer thickness d can be calculated from the mass m as d = m/(F·ρ), where F is the area and ρ is the density of the layer material. However, for thin layers, the true area is often not known due to the roughness of the substrate, and the macroscopic concept of density becomes meaningless for monatomic layers. Nevertheless, weighing can still provide the "average mass coverage" of the layer in mass per cm² of macroscopic surface area.
In this work, a different approach was taken to find a weighing method that allows for high measurement accuracy, robustness, and general applicability. Quartz plates of the Dickson oscillation type (AT and BT cuts) were found suitable for weighing thin layers, as their natural frequency depends not only on the plate thickness but also on the thickness of foreign layers on the plate surface.
The dependence of the natural frequency on the thickness of foreign layers was investigated to clarify how quartz can be used for weighing thin layers. The natural frequency of a quartz plate with a foreign layer is given by f = v_tr/(2·d) = N/d, where v_tr is the speed of the transverse elastic wave and N is a frequency constant. For the AT and BT cuts, N has values of 1670 kHz·mm and 2500 kHz·mm, respectively.The use of piezoelectric quartz plates for the weighing of thin layers and for micro-weighing is discussed. When a foreign layer is deposited on a quartz plate excited to its free oscillation frequency, the plate's frequency changes due to the increased oscillating mass. Since the frequency change of a quartz can be measured very precisely, this leads to a highly sensitive method for weighing thin layers. The mass coverage of the foreign layer and the frequency change are proportional. The proportionality constant can be calculated from the quartz's natural frequency, eliminating the need for empirical calibration in layer weighing.
The accuracy of the layer weighing method is mainly limited by the temperature dependence of the quartz's natural frequency. At a temperature fluctuation of 1°C, the accuracy is approximately ±4×10⁻⁹ g·cm⁻², corresponding to an average thickness of 0.4 Å at a density of 1 g·cm⁻³. This method was also used for direct weighing of a mass (micro-weighing), achieving an accuracy of 10⁻¹⁰ g.
Most investigations of thin layers require the determination of the layer thickness or an equivalent parameter. Weighing is one method for measuring the thickness of thin layers. The layer thickness d can be calculated from the mass m as d = m/(F·ρ), where F is the area and ρ is the density of the layer material. However, for thin layers, the true area is often not known due to the roughness of the substrate, and the macroscopic concept of density becomes meaningless for monatomic layers. Nevertheless, weighing can still provide the "average mass coverage" of the layer in mass per cm² of macroscopic surface area.
In this work, a different approach was taken to find a weighing method that allows for high measurement accuracy, robustness, and general applicability. Quartz plates of the Dickson oscillation type (AT and BT cuts) were found suitable for weighing thin layers, as their natural frequency depends not only on the plate thickness but also on the thickness of foreign layers on the plate surface.
The dependence of the natural frequency on the thickness of foreign layers was investigated to clarify how quartz can be used for weighing thin layers. The natural frequency of a quartz plate with a foreign layer is given by f = v_tr/(2·d) = N/d, where v_tr is the speed of the transverse elastic wave and N is a frequency constant. For the AT and BT cuts, N has values of 1670 kHz·mm and 2500 kHz·mm, respectively.