Simulation of electrical properties of quartz crystal microbalance using multi-resonance thickness-shear mode technique

2016, accepted on 2 nd December 2016) ABSTRACT The use of quartz crystal microbalance (QCM) in chemistry, biophysics, microbiology and electronics has grown tremendously in recent years. In this paper, the properties of a QCM sensor (a system include QCM device and viscoelastic medium) operating in the range of 5 MHz to 35 MHz of Multi-resonance Thickness-Shear Mode (MTSM, n = 1, 3, 5, 7) are described. We calculate the changes both in resonant frequencies and attenuation of the QCM. The penetration depth of the shear waves propagating from quartz into loaded thin film varies in different values due to the harmonics, from which we infer the properties of the loaded thin film. The multi-harmonic operation of QCM was presented to collect the information of the loaded thin film on QCM’s electrode. This enables a “virtual slicing technique” because a harmonic relates to a different penetration depth even with the same material. The theoretical analysis of MTSM has been developed to model and simulate the signature of the sensor responses at harmonic frequencies. The signatures of the evaporation- induced deposition processes were investigated by studying the effect of này cho phép một "kỹ thuật lát mỏng ảo" bởi vì trên cùng một loại vật liệu thì độ sâu lan truyền của mỗi hài cũng khác nhau. Các phân tích lý thuyết của MTSM đã được phát triển để mô hình hóa và mô phỏng các dấu hiệu phản hồi của cảm biến tại tần số của các bậc hài. Dấu hiệu của quá trình lắng đọng trên bề mặt linh kiện QCM được xác định bằng cách nghiên cứu ảnh hưởng của độ dày


INTRODUCTION
The Quartz Crystal Microbalance (QCM) is a very sensitive device that measures the mass by detecting the change in vibrating frequency of the quartz crystal. The change in the frequency and attenuation of the crystal is proportional to the added mass and the viscosity of the medium. To design QCM usable in damping media like a sensor, simulation tools to predict its behavior is very useful.
There are a large number of published papers describing the interaction of proteins and peptides with polymeric and planar thin films (Briseno et

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QCM combined with thin interfacial chemistries has been used to measure the transfer efficiency of a HSA-octadecylamine Langmuir-Blodgett (LB) film from the subphase interface to the gold electrode surface (Yin et al., 2005), confirming the protein resistance of poly(ethyleneglycol) (PEG) SAMs (Menz et al., 2005) and supported bilayers of eggphosphatidylcholine (PC) lipids (Glasmastar et al., 2002). QCM was also used to characterize the adsorption kinetics of unfolded and folded low molecular weight proteins to hydrophobic SAM surfaces (Otzen et al., 2003). He  This paper introduces the model which provides the evaporation-induced deposition processes of the film loaded on quartz by varying the thickness and stiffness of the medium. The main objective of the work is to simulate of MTSM sensor loaded with viscoelastic (VE) mediums but the geometrical (thickness) and the mechanical (density) properties of this medium will change following the evaporation-induced deposition processes.
Using the boundary condition, Maxwell's model and the equivalent circuit, we can find the attenuation, frequency shift which contain the information of the electrical properties by calculating by Matlab software. Electrical characteristics of the QCM sensor are depicted.

THEORY
A QCM consists of a thin AT cut -quartz crystal disk with two electrodes of the quartz ( Fig.1) [3]. Due to the piezoelectric properties and crystalline orientation of the quartz, a voltage applied to these electrodes results in a shear deformation of the crystal.
The resonant frequency f 0 of the quartz is given by: d: is the thickness of the QCM υ q : is the velocity of the acoustic wave propagation in quartz.
Sauerbrey [1] showed that the frequency change caused by an addition mass on that resonator is presented by: Which means that the variation in resonant frequency (Δf 0 ) in terms of the mass variation (∆m) is proportional to the square of the resonant frequency (f 0 ) and inversely proportional to the electrode area (A), the density (ρ q ) and the viscosity (μ q ) of liquid. In other words, higher resonant frequency and smaller electrode area will result in a higher sensitivity. Sauerbrey‗s relation is extended for use with elastic films by Miller and Bolef [4] and simplified by Lu and Lewis [5]. Until recently, excessive viscous loading was believed to prohibit the use of the QCM in liquids. In fact, this is still possible and the response of the QCM is sensitive to mass changes at the solid-solution interface.
When the QCM operates in a solution, the frequency is decreased depending on the viscosity and the density of the solution. This problem was first studied by Glassford [6], and later by Kanazawa and Gordon [2]. Kanazawa realized that the solution properties influenced the crystal resonance frequency and the resonance frequency shift is calculated by: Where η l and ρ l are the viscosity and density of liquid contact with the electrode and η q , ρ q are the viscosity and density of quartz.
The measured frequency shift is changed by the density and the viscosity of the liquid. When the QCM works in a liquid, the maximum displacement happens on the surface. This makes the device sensitive to a superficially added mass which causes a change in the resonant frequency. To use QCM as a biosensor, the crystal is coated with a thin layer antigen and is used to detect antibodies.  QCM devices can be operated not only at fundamental harmonic but also at higher harmonic. As higher harmonics are applied, the frequency shift and attenuation represent the mechanical properties of the loaded thin fim of the different distance from the surface of quartz due to the different penetration depth of the acoustic wave through the medium. Fig. 3 shows the principles of this concept [7]. For example, if the medium has different mechanical properties through the thickness, then it can be observed by analyzing the different responses of the MTSM sensor at each harmonics. METHOD QCM or MTSM sensor was used as a biosensor and the application process is the evaporation-induced deposition process whereby atoms or molecules in a liquid state gain sufficient energy to enter the gaseous state and leaving a thin-film. Especially, during the evaporation-induced deposition process of biological samples, there are two major processes involved: evaporation of a solution and deposition of proteins on the surface of the sensor substrate.
Since the response of the MTSM depends on the interfacial processes, such as mass accumulation (density) or changes in mechanical and geometrical properties (elastic stiffness, viscosity, and thickness). In this paper, only the thickness (represent to geometrical properties) and density (represent to mechanical properties) were studied and analyzed using theoretical and simulation method. The output signals are the frequency shifts, the attenuation and the penetration depth at harmonics.  The proposed geometry of the composite QCM/viscoelastic mediums by [2] is used in this study (Fig. 5). The mathematics using in this geometry is simple.
The origin is at the interface between the quartz and the film. The film is characterized by its density ρ f , its shear modulus μ f and its viscosity η f . The quartz parameters include its density ρ q , its shear modulus c 66 , its appropriate piezoelectric constant e 26 , its relative permittivity ε 22 and its viscosity η q . For purpose in fabrication, we have chosen the series of resonance of unloaded quartz at exactly 5 MHz.
The shear waves in both the quartz and the over layer are the sum of a wave travelling in the +y direction and another in the -y direction and have the form e iωt . For the quartz, the amplitude of the wave travelling in the +y direction is A and in the -y direction is B. Similarly, the wave amplitudes in the over layer are C and D. The wave vector for the shear wave in the quartz is k q and the over layer is k f . The shear wave spreading in the quartz have the following forms: and the over layer: Where A and h s are the area of the electrode and the thickness; ε22, μq, and ηq are the dielectric permittivity, shear stiffness and effective viscosity of the MTSM sensor, respectively. Zt indicates the total electrical impedance of the MTSM. S21 means the forward transmission parameter.
The relative change in the resonant frequency (Δf) is the real part of this equation (9),

RESULTS AND DISCUSSION
We have developed a program using Matlab software to trace out the effect of change in the thickness and density on the MTSM response and effect of changes in density on the MTSM response. The mechanical properties of AT-cut quartz were shown on Table 1. Piezoelectric constant (S/m 2 ) 334x10 - 6 2.648 2.947x10 10 9.2475x10 -3 3.982x10 -11 9.53x10 -2

Effect of film's thickness
In this section, evaporation-induced deposition process of the films has been simulated by only varying the thickness. The input mechanical properties of the thin film loaded were shown in Table 2.
In this case, the film is a Newtonian liquid because of the low concentration of the solutes in the solution. The stiffness was equal to zero and the density was 1000 kg/m 3 . Due to the evaporation process of the solvent through the liquid surface the thickness of the sample changes. Therefore, only the thickness of the sample was varied from 10 µm down to 100 nm for the simulations. Fig. 7, 8, 9 show the simulation of the MTSM sensor of harmonic responses for liquids of different viscosity. Gray arrows in each graph show the direction of changes in the thickness decreasing during the evaporation process. Fig. 7 show the response of the MTSM sensor when the viscosity of the VE load is the same as water at 0.001kg/ms. As the evaporation of the solvent is continuous, the concentration of the solute starts to increase and the increment of solute affects the viscosity of the solution to rise. Fig. 8, 9 show the response of MTSM sensor with the higher viscosity, 0.01 and 0.1 kg/ms.  The simulation results on Fig. 7, 8, 9 show the same trend. Firstly, it starts with stabilized response when the thickness is much larger than the penetration depth. Secondly, as the thickness of the VE film reaches close to couple of the penetration depth, the response of MTSM sensor starts to oscillate in both relative changes in resonant frequency (∆f) and attenuation (α). Finally, when the thickness of the VE film becomes smaller than the penetration depth, it shows the both Sauerbrey mass effect and Kanazawa viscous effect: decrease in both relative ∆f and α, as the thickness becomes smaller. Table 3 shows the penetration depth (δ) of acoustic shear waves in each simulation.

Effect of film's density
In this section, the evaporation-induced deposition process of biological films has been simulated by varying the density of the film. The mechanical properties of Newtonian Liquid was shown in Table 4.
In this case, the density changed from 500 to 2000 kg/m 3 for the simulation to be in the realistic range. Fig. 10, 11, 12 show the effect of density in the response of the MTSM sensor. The results showed either a typical Sauerbrey effect (effect of mass due to change the density) or the Kanazawa effect (effect of viscous due to change the density).
In Fig. 10 and 11 the MTSM sensor treats the VE film as a load with an infinite thickness film and the Kanazawa viscous effect is showed in the graphs. As the density of the VE film increase, the relative changes in ∆f and α are also increased. As an acoustic signature, the attenuation of the higher harmonic responses, such as 5 th and 7 th harmonics, seems not sensitive to the changes in the density of the medium, and the attenuation of the lower harmonics, such as 1 st and 3 rd harmonics, shows the density effect (as density increases attenuation also increases due to the Kanazawa viscous effect).  In Fig. 12, the thickness of the VE film is always much smaller than the penetration depth of the film, except the 7 th harmonic. At 1 st , 3 rd , and 5 th harmonics, the graphs show the typical Sauerbrey Mass effect. At the 7 th harmonic, as the density increases, the penetration depth of the MTSM sensor becomes close to the thickness of the film and this causes the oscillatory behavior of the MTSM sensor.  The relationships between the frequency shift, the attenuation of MTSM sensor and the thickness, density of film at harmonics have been illustrated. A knowledge of the properties of the loaded film is very useful in explaining the result of electrical properties measurements. This result will help choosing suitable polymers in fabrication and application QCM as biosensor.