Analysis of the Uniformization of the QCM Mass Sensitivity Distribution through a Dot Multiring Electrode Structure

Abstract

In this paper, to improve the uniformity of the quartz crystal microbalance (QCM) mass sensitivity distribution, the effect of the size of dot ring electrode and dot double-ring electrode on the mass sensitivity distribution is analyzed theoretically from the perspective of the electrode width ratio, the width of the partially electroded region, and the electrode thickness. Within a certain range of electrode thickness, there is an optimum electrode width ratio to obtain a relatively uniform distribution. As long as the width of the partially electroded region is not too large or too small, it has no significant influence on the uniformity of the mass sensitivity of the optimum electrode size. The dot triple-ring electrode is proposed and the comparison of the uniformity between the three electrode structures indicates that more division of the electrode region can greatly improve the uniformity of the mass sensitivity distribution. This research provides a new direction for the uniformization of QCM mass sensitivity distribution.

Advances in the Mass Sensitivity Distribution of Quartz Crystal Microbalances: A Review

“…Based on Gao et al, other additional configurations of electrode shapes have been designed to obtain uniform mass sensitivity distribution [ 49 , 51 , 52 , 53 ]. For example, Jiang et al used mathematical models and the finite element method (FEM) to further analyze in depth the mass sensitivity function distribution of the double-ring electrode QCM [ 52 ].…”

Analysis of the Effect of Electrode Materials on the Sensitivity of Quartz Crystal Microbalance

“…According to previous works, the mass sensitivity of QCM exhibits a Gaussian distribution, which can be calculated by the following formula [ 13 , 18 , 19 ], where and are the mass sensitivity distribution and Sauerbrey sensitivity constant, respectively. and are the distance from the electrode center and the particle displacement function, respectively.…”

Design and Analysis of Quartz Crystal Microbalance with a New Ring-Shaped Interdigital Electrode

“…The relationship between the change in resonance frequency and mechanical load is shown as follows [ 20 ]: where is the mass sensitivity function, is the added mass on surface, and are the position of the added mass in polar coordinates. When QCM works under the fundamental frequency vibration, the mass sensitivity function is as follows [ 11 , 17 ]: where is the vibration displacement function of the particle on the surface. The denominator is the integral of the total surface effective particle amplitude intensity.…”

“…Vibration displacement on surface of QCM with interdigital electrode can be expressed by the solution of Bessel equation [ 17 ]: where and are the Bessel functions of order-zero of the first and second kinds, respectively. and are the modified Bessel functions of order-zero of the first and second kinds, respectively.…”

“…The subsequent research mainly focused on optimizing the thickness and geometry of the ring electrode to further unify the mass sensitivity [ 13 , 14 , 15 , 16 ]. The bimodal distribution was further modified into three and four peaks through dot ring and dot double-ring by Gao et al [ 9 ], Huang et al [ 17 ]. They compared the influence of electrodes with different sizes on the multi-peak mass sensitivity distribution through theoretical analysis.…”