The transfer matrix method [22�C24] is much more complicated although it has a more accurate solution. In this work, the amount of absorbed gas is tiny, the solution of Wohltjen’s method, which is based the perturbation theory, has enough accuracy; therefore, Wohltjen’s method is adopted due to its simple expression. We assume that the absorbed gas forms an isotropic, non-piezoelectric, non-conducting layer with a thickness of h, a density of �� on the SAW detector surface. The change in oscillation frequency can be described by :��f=(k1+k2)f02��h?k2f02��h4�̦�02(��+�̦�+2��)(1)where k1 and k2 are the coupling constants determined by the different displacement components of SAW in the substrate; f0 is the unperturbed oscillating frequency of the SAW oscillator, which is determined by the propagation velocity of SAW and the period of the IDTs fabricated on the surface of the piezoelectric substrate; �� and �� are the shear modulus and Lame constant of the layer; ��0 is the unperturbed velocity of SAW in the piezoelectric substrate.
The first term in Equation (1) represents the frequency change caused by mass loading and the second term depends on the acoustic wave coupled into the layer. Because the layer formed by adsorbed gas is very thin, it can be seen as a simple mass load attached to the surface of the SAW device. Thus Equation (1) can be simplified as:��f=(k1+k2)f02��(2)where �� = ��h is the areal density of the layer formed by the adsorbed gas. Equation (2) means that the sensor output is proportional to the quantity of the mass loaded on the surface of a SAW device, and it is the theoretical basis for the detection of SAW sensors.
2.2. Adsorption Mechanism of Gas on the Surface of SolidsDue to intermolecular forces or chemical bonding force, when a gas contacts with the surface of a solid, part of the gas molecules will stay on the solid surface for some time. This phenomenon is called adsorption. The adsorption generated by the intermolecular force is a physical AV-951 adsorption; the adsorption generated by chemical bonding force is a chemical adsorption. During the process of chemical adsorptions, chemical reactions will produce new molecules from the molecules of absorbed gas and the molecules in the solid surface, which means that the absorbed gas will be changed into a new material. Since chemical bonds are much stronger than molecular diffusions, chemical adsorptions are almost irreversible at room temperature and pressure, which means that no desorption will happen when the gas leaves. Thus, the sensor based on chemical adsorption is unrepeatable. Most of SAW gas sensors are required to be repeatable, so the adsorption is a physical one.