Characteristics Research of a High Sensitivity Piezoelectric MOSFET Acceleration Sensor

Abstract

In order to improve the output sensitivity of the piezoelectric acceleration sensor, this paper proposed a high sensitivity acceleration sensor based on a piezoelectric metal oxide semiconductor field effect transistor (MOSFET). It is constituted by a piezoelectric beam and an N-channel depletion MOSFET. A silicon cantilever beam with Pt/ZnO/Pt/Ti multilayer structure is used as a piezoelectric beam. Based on the piezoelectric effect, the piezoelectric beam generates charges when it is subjected to acceleration. Due to the large input impedance of the MOSFET, the charge generated by the piezoelectric beam can be used as a gate control signal to achieve the purpose of converting the output charge of the piezoelectric beam into current. The test results show that when the external excitation acceleration increases from 0.2 g to 1.5 g with an increment of 0.1 g, the peak-to-peak value of the output voltage of the proposed sensors increases from 0.327 V to 2.774 V at a frequency of 1075 Hz. The voltage sensitivity of the piezoelectric beam is 0.85 V/g and that of the proposed acceleration sensor was 2.05 V/g, which is 2.41 times higher than the piezoelectric beam. The proposed sensor can effectively improve the voltage output sensitivity and can be used in the field of structural health monitoring.

1. Introduction

Micro-electro-mechanical system (MEMS) acceleration sensors, with the advantages of low cost, low power consumption, high compatibility with integrated circuit (IC) process and high integration [1,2,3,4], have a wide range of applications in automotive electronics, structural health monitoring, navigation and other fields [5,6,7,8]. MEMS acceleration sensors usually include piezoresistive [9,10], capacitive [11] and piezoelectric acceleration sensors [12,13]. Piezoresistive accelerometer usually consists of a deformable structure and varistors. Under the action of external acceleration, the deformation of the deformable structure causes the resistance of the varistor to change, thereby measuring the acceleration. The varistors are usually made into a Wheatstone bridge structure to improve the output sensitivity. The piezoresistive accelerometer has the advantages of good stability, wide measurement range, and is also limited by ambient temperature [14,15,16]. A capacitive acceleration sensor is composed of fixed plates and movable plates. The gap or area of the plate capacitor changes while the external acceleration is applied. The applied acceleration is obtained by measuring the change of capacitance. High sensitivity and zero frequency response are its advantages, while its disadvantages are high impedance and nonlinearity [17,18,19]. The working principle of the piezoelectric acceleration sensor is similar to that of the piezoresistive type, but the difference is that the piezoresistive material is replaced by piezoelectric material. Compared with piezoresistive and capacitive MEMS acceleration sensors, piezoelectric MEMS acceleration sensors have advantages of low power cost and high range of applying frequency; at the same time, they are also limited by high output impedance, weak output signal and so on [20,21,22,23].

The researchers are committed to improving the structure of the piezoelectric acceleration sensor so as to improve its performance, especially its sensitivity. For example, ** ** lithium as an acceptor impurity, the resistivity of ZnO is increased, thereby enhancing its piezoelectric properties. The piezoelectric beam is designed to be 9800 × 5800 × 500 μm³ in size. Figure 2c shows the dimension of the cantilever beam. l_b, w_b and h_b are the length, width and height of the cantilever beam, respectively. l_m, w_m and h_m are the length, width and height of the proof mass, respectively. l_b × w_b × h_b was designed to be 6000 × 2400 × 80 μm³, l_m × w_m × h_m was designed to be 1000 × 2700 × 395 μm³. After the piezoelectric beam was manufactured, it was rigidly pasted on the customized test printed circuit board (PCB), and the piezoelectric beam’s electrodes were connected with the PCB plate electrodes by a chip press welder (KNS4526, Kullicke & Soffa, Haifa, Israel).

2.2. Operating Principle

As shown in Figure 3a, the piezoelectric beam does not deform without external force. The centers of positive and negative charges in the piezoelectric layer coincide with each other; the whole piezoelectric layer is electrically neutral and there are no charge outputs. The PMAS also has a certain output when it is not affected by acceleration due to the existence of a conductive channel in the N-channel depletion MOSFET even when the gate voltage is 0. When external acceleration is applied, according to Newton’s first and second laws, the proof mass will produce forces opposite to the acceleration direction due to the inertia, which can cause the piezoelectric beam to be deformed. At this time, the bending creates the electric dipole moment in the piezoelectric layer, forcing the positive and negative charge centers to separate. The same amount of charges of different signs are generated on the upper and lower surfaces of the piezoelectric layer. The generated charge is used as the gate signal of the MOSFET, which can directly control the width of the channel, thereby controlling the drain current of the MOSFET.

The stress analysis of the piezoelectric beam is shown in Figure 4. d_ZnO is the distance from the ZnO thin film to the bottom of the Si substrate, d_n is the distance from the neutral plane of the multilayer structure to the bottom of the Si substrate, h₁, h₂, …, h₆ represent the thickness of Si, SiO₂, Ti, Pt, ZnO and Pt layers, respectively.

The main assumptions are as follows: (1) since the length and width are far greater than the thickness of the cantilever beam, it is considered that the cantilever beam has pure bending deformation and ignores the shear stress; (2) the beam bending caused by the residual stress is ignored; (3) the beam bending caused by the residual stress is ignored; (4) it is assumed that there is no relative sliding between each thin films; (5) the cantilever beam is in an open environment and there are no upper and lower fixed plates, so the influence of air dam** is ignored [27,28,29].

According to the Euler-Bernoulli’s equation, when the free end of the cantilever beam is subjected to a concentrated transverse force F, the stress on the cross section A of ZnO thin film is:

$${\sigma }_{\mathrm{A}}=\frac{M_{\mathrm{A}}}{I}\left|d_{\mathrm{ZnO}}-d_{\mathrm{n}}\right|=\frac{F\cdot x}{I}\left|d_{\mathrm{ZnO}}-d_{\mathrm{n}}\right|$$

(1)

where M_A is the bending moment, I is the moment of inertia of the multilayer structure.

The equivalent width of layer i relative to Si substrate is:

$$w_{{}_i}^{\prime }=\frac{E_i}{E_{\mathrm{Si}}}{w}_{\mathrm{Si}},\hspace{1em}\mathrm{i}=1,2,\dots ,6$$

(2)

where w^′_i is the width of each thin film, E_i is the young’s modulus, i represents Si, SiO₂, Ti, Pt, ZnO and Pt layers, respectively.

Therefore, the equivalent sectional area S_i can be expressed as:

$$S_i=w_i\cdot h_i,\hspace{1em}i=1,2,\dots ,6$$

(3)

The equivalent second moment of inertia of layer i is:

$$I_i^{\prime }=\frac{h_i^3}{12}{w}_i,\hspace{1em}i=1,2,\dots ,6$$

(4)

The distance from the i layer to the bottom of Si substrate is:

$$z_i={\displaystyle \sum _{i=1}^6{h}_i-\frac{h_i}{2}}$$

(5)

The distance from the neutral plane of the multilayer structure to the Si substrate is:

$$z^{\prime }=\frac{{\displaystyle \sum _{i=1}^6{S}_i{d}_i},}{{\displaystyle \sum _{i=1}^6{S}_i}}$$

(6)

The second moment of inertia is:

$$I^{\prime }={\displaystyle \sum _{i=1}^6\left[I_i+S_i{\left(z_i-z^{\prime }\right)}^2\right]}$$

(7)

Substituting Equations (6) and (7) into (1), the cross-section stress of ZnO is:

$$\sigma =\frac{F\cdot x\cdot \left|d_{\mathrm{ZnO}}-d_{\mathrm{n}}\right|}{{\displaystyle \sum _{i=1}^6\left\{\frac{h_i^3{w}_i}{12}+S_i\left[\left({\displaystyle \sum _{i=1}^6{h}_i-\frac{h_i}{2}}\right)-\frac{{\displaystyle \sum _{i=1}^6{S}_i{d}_i},}{{\displaystyle \sum _{i=1}^6{S}_i}}\right]\right\}}},\hspace{1em}0\le x\le l$$

(8)

According to the Hooke’s law and the theories in mechanics of materials, a deflection δ will appear when a force F is applied at the free end of the cantilever beam, and the deflection δ of the free end can be expressed as [30,31]:

$$\delta =\frac{F}{k}=\frac{F{l}_{\mathrm{b}}{}^3}{3EI}=\frac{4F{l}_{\mathrm{b}}{}^3}{E{w}_{\mathrm{b}}{h}_{\mathrm{b}}^3}$$

(9)

where k is the stiffness of the cantilever beam.

The fundamental resonant frequency is [32]:

$$f=\frac{{\alpha }_n^2}{2\pi }\sqrt{\frac{EI}{m{L}^4}}$$

(10)

where E is the modulus of elasticity, I is the area moment of inertia, α_n is a constant which its value depends on the mode of cantilever beam’s vibration, m is the mass of the cantilever beam, L is the length of the cantilever beam.

Considering the influence of the mass proof on the resonant frequency of cantilever beam, the first mode resonant frequency of the cantilever beam can be expressed as [33,34,35]:

$$f={\frac{1.875}{2\pi }}^2\sqrt{\frac{0.236EI}{{\left(l_b-l_m/2\right)}^3\left(0.236\rho h_b{w}_b\left(l_b-\frac{l_m}{2}\right)+\rho h_b{w}_b\frac{l_m}{2}+\rho h_m{w}_m{l}_m\right)}}$$

(11)

where ρ is the density of Si. The moment of inertia of multilayer structure is ignored due to the thickness of the multilayer structure being much less than that of the cantilever beam.

It can be seen that l_c is inversely proportional to the f frequency of the cantilever beam, and the change of l_c has a greater impact on resonant frequency. Based on the piezoelectric effect, the surface charge density of ZnO is [26]:

$$D_3=d_{31}\sigma$$

(12)

Therefore, under the external acceleration, the charges generated by the piezoelectric beam are:

$$\begin{array}{ll}q& ={\displaystyle {\int }_0^{w_b}{\displaystyle {\int }_0^{l_b}{D}_{3}dxdy}}\\ & ={\displaystyle {\int }_0^{w_b}{\displaystyle {\int }_0^{l_b}{d}_{31}\sigma dxdy}}\\ & ={\displaystyle {\int }_0^{w_b}{\displaystyle {\int }_0^{l_b}\frac{d_{31}Fx\left|d_{\mathrm{ZnO}}-d_{\mathrm{n}}\right|}{{\displaystyle \sum _{i=1}^6\left\{\frac{h_i^3{w}_i}{12}+S_i\left[\left({\displaystyle \sum _{i=1}^6{h}_i-\frac{h_i}{2}}\right)-\frac{{\displaystyle \sum _{i=1}^6{S}_i{d}_i},}{{\displaystyle \sum _{i=1}^6{S}_i}}\right]\right\}}}dxdy}}\\ & =\frac{w_b{l}_b^2{d}_{31}F\left|d_{\mathrm{ZnO}}-d_{\mathrm{n}}\right|}{2{\displaystyle \sum _{i=1}^6\left\{\frac{h_i^3{w}_i}{12}+S_i\left[\left({\displaystyle \sum _{i=1}^6{h}_i-\frac{h_i}{2}}\right)-\frac{{\displaystyle \sum _{i=1}^6{S}_i{d}_i},}{{\displaystyle \sum _{i=1}^6{S}_i}}\right]\right\}}}\end{array}$$

(13)

The piezoelectric beam can be approximately considered as a parallel plate capacitor with a dielectric inside, so the output voltage V_B of the piezoelectric beam is:

$$V_{\mathrm{B}}=\frac{q}{C}$$

(14)

In this case, due to the MOSFET works in the triode region, the relationship between source drain current I_DS and gate voltage V_GS can be expressed as follows [36]:

$$I_{\mathrm{DS}}=\frac{{\mu }_{\mathrm{n}}W{C}_{\mathrm{ox}}}{L}\left[\left(V_{\mathrm{GS}}-V_{\mathrm{T}}\right)V_{\mathrm{DS}}-\frac{1}{2}{V}_{\mathrm{DS}}^2\right]$$

(15)

where, μ_n is dependent effective mobility, W is the channel width, L is the effective channel length, C_ox is the insulation capacitance, V_GS is the gate voltage which is equal to V_B, V_T is the threshold voltage.

The output voltage of PMAS is:

$$V_{\mathrm{out}}=V_{\mathrm{DD}}-V_{\mathrm{R}}=V_{\mathrm{DD}}-I_{\mathrm{DS}}{R}_{\mathrm{L}}$$

(16)

Therefore, when the piezoelectric beam is connected to the gate of MOSFET, the output voltage of the piezoelectric beam is equal to V_GS. With Equations (13)–(16), the relationship between V_out and F is:

$$V_{\mathrm{out}}=V_{\mathrm{DD}}-\frac{{\mu }_{\mathrm{n}}W{C}_{\mathrm{ox}}}{L}\left[\left(\frac{q}{C}-V_{\mathrm{T}}\right)V_{\mathrm{DS}}-\frac{1}{2}{V}_{\mathrm{DS}}^2\right]R_{\mathrm{L}}$$

(17)

It can be seen from Equation (17) that the output voltage of the PMAS is proportional to the channel width-to-length ratio of the MOSFET.