Mass Sensitivity Analysis of a Newly Developed Quartz Crystal Microbalance with Ring-Dot Electrode Configuration and Reduced Mass Loading Area

Quartz Crystal Microbalance (QCM) is used for detecting microgram level mass changes in gas and liquid phase. Conventional QCM design comprises a circular electrode configuration with an evenly distributed mass loading area. However, their mass sensitivity distribution is found to be non-uniform due to the inherent energy trapping effect. In this paper, the recently developed QCM with a ring electrode and a ring-dot electrode configuration are evaluated. It is shown that this new configuration offers the ability to achieve a uniform mass sensitivity distribution, while attaining a comparable mass sensitivity for a reduced mass loading area. Finite Element Analysis is used to design and evaluate the conventional circular electrode QCM, and the proposed ring electrode and ring-dot electrode QCM configurations, where the mass loading area is reduced by 25% compared with the conventional sensor. Simulations are conducted to determine the sensor’s resonant frequency shifts for an added mass per unit area of 20 μg/mm2. The results indicate that newly designed ring and ring-dot electrode configurations operate at a higher resonant frequency. The observed frequency shift for the designed circular electrode, ring electrode, and ring-dot electrode configurations on a 333 μm thick quartz substrate are 85 kHz, 84 kHz, and 82 kHz, respectively. It is shown that the ring electrode and new ring-dot electrode configurations achieve a higher resonant frequency and offer a comparable sensing performance despite comprising of over 25% reduced mass loading area, in comparison to the conventional circular electrode configuration.

• To design a single channel Quartz Crystal Microbalance with conventional circular electrode, ring electrode and the recently developed ring-dot electrode configuration and simulate its resonant frequency and frequency shift for an added mass using Multiphysics simulations.
• To investigate the influence of mass loading area on frequency shift of the QCM in order to potentially improve the device mass sensitivity while utilizing a reduced mass loading area.
• To analyze the influence of the electrode dimensions of the ring electrode and the new ring-dot electrode configuration to achieve a higher resonant frequency in comparison to the conventional design, and potentially improve the device sensing performance for a reduced mass loading area.

Objective
Quartz Crystal Microbalance (QCM) is a micromachined gas sensor that can be utilized for measuring microgram level mass changes on the basis of change in frequency.

Introduction to Quartz Crystal Microbalance Gas Sensors
• It operates on the principle of the piezoelectric effect and comprises of a quartz crystal sandwiched between a top sensing electrode and a bottom reference electrode.
• Gold, Platinum and Silver are widely employed as metal electrodes for the QCM based on their high conductivity and inertness property.
• A sensing material is coated on the top sensing electrode which acts as a mass loading area in order to detect analytes. • Alternating voltage is applied to the QCM electrodes which creates an electric field thereby inducing a stress in the crystal which causes mechanical vibration or oscillation.
• AT cut quartz crystals vibrate in an antiparallel fashion and hence produce thickness shear oscillations. This ensures frequency stability over a temperature range of -45 to 50°C and thus, can be used for detection in room temperature.
• The vibrational amplitude of the quartz is higher near the centre of the crystal and reduces in a gaussian pattern towards the edges. This is due to the energy trapping effect.

Principle of Operation of QCM Gas Sensors
• The presence of the analyte on the mass loading area causes a change in the resonant frequency of the crystal as a result of additional stress. This change in frequency due to an added mass is utilized to identify the analyte.
• The change in the resonant frequency of the crystal due to mass deposition gives rise to a relation between mass and frequency which is governed by the Saurebrey equation, • The sensitivity of a device is the ability to detect small changes that are observed in its application. For QCM mass sensors, it is the ability to detect surface mass changes by the resonant frequency shift (Δf).

Resonant Frequency Shift due to an Added Mass
• COMSOL Multiphysics 5.5 is utilized to build and simulate the resonant frequency of a QCM in the 3D space dimension.
• Resonant frequency of QCM is simulated and obtained by Adaptive frequency sweep. The frequency where maximum displacement is observed denotes the resonant frequency.
• In this work the frequency shift (Δ ) for an added mass ( ) is utilized to determine the device's sensing performance.

∝
• The 'added mass' entity of COMSOL is used to define a mass on the mass loading area of the QCM based on the principle, is mass acting upon the selected surface 'A' , ' ' is the mass per unit area, 'ω' is the angular frequency, 'u' is the displacement and 'a f ' is external force contribution such as gravitational acceleration.

Conventional Circular Electrode Configuration
• The circular electrode configuration is the conventional QCM electrode configuration.
• In this design, the entire top electrode is utilized for mass loading, thereby ensuring a higher frequency shift. However, it also consists of an unevenly distributed mass sensitivity due to energy trapping.
• The parameters used to build the circular electrode QCM are mentioned in Table 1.

Circular Electrode
Quartz Crystal    • The resonant frequency shift due to an added mass of 20 μg/mm 2 on the top electrode is determined for the different mass loading area.

Analysis of Effect of Mass Loading Area
• Utilizing the QCM with conventional circular electrode configuration, an analysis is performed to determine the effect of mass loading area on the frequency shift (Δf) of the QCM.

•
The mass loading area is specified as a boundary on top of the top electrode representing a polymer layer of null thickness (no height). • The frequency shift also increases towards the edge of the electrode from 3.75 to 4.25 mm radius of mass loading area.

Analysis of Effect of Mass Loading Area
• The analysis results provides a scope for modifying the QCM electrode configuration to potentially achieve a higher frequency shift for a lesser mass loading area by selectively electroding the QCM surface. 13

Ring Electrode Configuration
• The ring electrode design is proposed to improve the mass sensitivity distribution across the QCM electrode by reconfiguring the electrode area, and potentially achieving a higher resonant frequency.
• The parameters used to build the QCM is based on a conventional 5 MHz circular QCM and are mentioned in the table 3. The outer electrode radius is fixed at 4.25 mm for fair comparison with the circular electrode design.

Ring Electrode
Quartz Crystal

Ring Electrode Configuration -Effect of Ring width
• This analysis was performed in order to determine the effect of the ring electrode width on the frequency shift (Δf) of the QCM with ring electrode configuration.
• In this analysis, the ring electrode width was varied for different values ranging from 0.75 mm to 2.5 mm.
• The resonant frequency and frequency shift was determined for an added mass per unit area of 20 μg/mm 2 .  16

Ring-Dot Electrode Configuration
• The new Ring-Dot electrode configuration was proposed to improve the mass sensitivity distribution of the ring electrode, while ensuring a higher mass sensitivity by adding a central dot (circular) electrode.
• The parameters used to build the QCM is based on a conventional 5 MHz circular QCM and are mentioned in the  • This analysis was performed in order to determine the influence of the ring electrode width on the frequency shift (Δf) of the ring-dot electrode configuration.
• In this analysis, the dot electrode radius was kept constant at 5 mm, while the ring electrode width was varied from 0.5 to 1.5 mm by a step of 0.25 mm.
• The observed simulation results are depicted in Table 6.  • This analysis was performed in order to determine the effect of the dot electrode radius on the frequency shift (Δf) of the ring-dot electrode configuration.
• The resonant frequency and frequency shift was determined for an added mass per unit area of 20 μg/mm 2 .
• In this analysis, the ring electrode width was kept constant at 0.75 mm, while the dot electrode width was varied from 0.5 to 3.5 mm.

Conclusion
• In this work, quartz crystal microbalance (QCM) with a conventional circular electrode, ring electrode and the recently developed ring-dot electrode configuration were designed, investigated and simulated for mass sensitivity analysis using Multiphysics simulations.
• The influence of mass loading area on frequency shift of the QCM was analyzed. The results indicated that mass loading on specific areas of the QCM electrode such as distance of 2.125 mm from center, and near the edges of the electrode can potentially improve the device sensing performance while utilizing reduced mass loading area. Based on this the ring electrode and the new ring-dot electrode configuration are built and investigated.
• The simulated ring electrode and the recently developed ring-dot electrode configurations achieve a higher resonant frequency and comparable frequency shift for an 17 to 30% reduced mass loading, when compared to the conventional design. This provides a scope to improve the mass sensitivity of the QCM by modifying parameters such ass the ring and dot electrode width and radius.