# Detecting Small Size Mass Loading Using Transversely Coupled SAW Resonator
## 1 Introduction  
The surface acoustic wave resonator (SAWR) was used mainly as an extremely narrow-band filter until [PERSON] reported its use to measure chemical vapors [1]. Since then, SAWRs have been widely used in the field of sensing for their advantages such as low loss, high sensitivity and stability. In recent years, SAWRs have received more attention in the field of biosensing, especially in the measurement of small mass loading [2, 3]. According to the resonance mode, SAWR could be sorted as a longitudinally coupled SAW resonator (LC-SAWR) and transversely coupled resonator (TC-SAWR). Normally, researchers take LC-SAWRs as sensor chips such as vapor detector [4], mass microbalance [5], PM2.5 detector [6], strain sensor [7, 8] and temperature sensors [9]. In these cases, the physical quantities measured were uniformly exerted on the surface of the acoustic wave device. However, in biological detection, the substances measured, such as cells and proteins, are of small size; thus, it is difficult for these substances to completely and uniformly cover the surface of the detector [10, 11, 12, 13]. In our previous work, we have discussed the effect of non-uniformly distributed loads on the LC-SAWR's response, which showed waveform distortions caused by small size mass loadings [14]. In order to achieve high performance in the sensing of small size mass loading, a TC-SAWR was proposed in this paper as a detector in order to conquer waveform distortion.  
When a LC-SAWR is working at its resonate mode, the device could be modeled as a combination of several independent channels [14]. If the load does not fully cover the device's aperture, it can only be applied to part of the channels. Then, the overall response of the device would be composed of the loaded channels' responses and thenon-loaded channels' responses. The center frequency of the loaded channel is lower than that of the no-loaded channel, resulting in waveform distortion. (Figure 1). For TC-SAWR, the acoustic wave resonates transversely in the aperture, forming resonance peaks of each mode (Figure 2). In this case, the device cannot be divided into multiple independent channels and needs to be analyzed integrally. As a result, the load acting on the TC-SAWR will change the resonance frequency of each mode, regardless of whether it covers the aperture completely or not, which avoids waveform distortion caused by the small size load.  
In the past, the one-dimensional coupled mode theory (1D-COM) has been used for the simulation and design of TC-SAWRs [15; 16]. However, this method can only compute a limited number of transverse modes; thus, it is not accurate enough to simulate the response of TC-SAWR. In addition, the 1D-COM theory is difficult with respect to modeling and simulating the device with small size loads. To solve these problems, we used the two-dimensional coupling-of-modes theory (2D-COM) and the finite element method (FEM) in order to obtain a more accurate simulation of TC-SAWR and to calculate the influence of small size loads on it.  
The experiment was implemented in this work to verify the simulation result. In the experiment, TC-SAWR with a SiO\({}_{2}\) cylinder attached to its surface was fabricated and measured.  
Figure 1: LC-SAWR with small size mass loading (**left**) and the waveform distortion (**right**).  
Figure 2: Basic structure of TC-SAWR and its transverse resonance modes.  
In this work, the effect of small size load attached to the TC-SAWR sensors were studied theoretically and experimentally. They consistently showed that the frequency response curve of TC-SAWR had no distortion under small size load, which illustrated the advantage of TC-SAWR in the field of biochemical detection.