Design and Fabrication of a Novel T-Shaped Piezoelectric ZnO Cantilever Sensor

Abstract

A novel T-shaped piezoelectric ZnO cantilever sensor for chem/bio-detection is designed and fabricated with MEMS technology. By using Rayleigh-Ritz method, the fundamental resonant frequency formula of T-shaped cantilevers is deduced for the first time and is validated by simulation results and experimental results. From this formula, we can easily find the superiority of adopting T-shape for the cantilevers. The complete process of the cantilever sensor is then successfully developed. The cantilever sensor is actuated by a layer of high-quality ZnO film with preferred (002) orientation, which is evaluated by SEM and XRD. The key step of the process is protecting the ZnO film from KOH etching by a novel and effective method, which has rarely appeared in the literature. Finally, this cantilever sensor is measured by a network analyzer, and it has a fundamental resonant frequency of 24.60 kHz. The cantilever sensor developed in this study illustrates the feasibility and potential for many miniaturized sensor applications.

1. Introduction

There is a dramatic and urgent demand to develop inexpensive, microfabricated, and extremely sensitive sensors for chem/bio-sensing. As mass sensitive sensors, microcantilever sensors have many advantages over other transducers. For example, these sensors have been shown to exhibit over two orders of magnitude greater absolute sensitivity such as quartz crystal microbalance (QCM), surface acoustic wave (SAW) devices, acoustic plate mode (APM) devices, chemiresistors, and flexural plate wave (FPW) oscillators [1]. So far, one of the most common ways to detect frequency shift or static deflection of cantilever-based sensors is optical inspection by means of a laser and position sensitive diode (PSD). However, laser and PSD are quite complex and bulky and almost impossible to minimize.

Another popular method without huge optical systems is by using piezoresistive layer on the cantilever itself. Any changes in the surface stress due to bending will cause an electrical output from the piezoresistive electrodes. The disadvantage of piezoresistive technique is that it requires passing a current through the cantilever for displacement measurements. This results in electronic noises and thermal drift in cantilever deflection.

In this study, we choose piezoelectric method for the purpose of simplifying and minimizing the sensors. To date, lead zirconate titanate (PZT) is one of the most widely exploited and extensively used piezoelectric materials. For example, Lee et al. [2] developed a PZT microcantilever biosensor for using in a lab-on-chip (LOC). However, there are a few unsolvable problems for PZT thin films: (1) the crystallization temperature of PZT is in the range of 600–700°C, which is not compatible with the CMOS integration [3] (2) a high electric field for poling is necessary, which may be difficult for PZT thin films that have some defects or pinholes [3] (3) the performance is gradually deteriorative due to aging effect [3] (4) PZT is highly toxic, and its toxicity is further enhanced due to its volatilization at high temperature particularly during calcination and sintering, causing environmental pollution [4].

Recently, ZnO has attracted a lot of attention because it is one of the pollution-free piezoelectric materials which do not suffer from the mentioned problems of PZT. ZnO finds applications in MEMS due to its unique combination of electrical, optical, and piezoelectric properties [5]. However, a serious problem which hinders its MEMS application is that ZnO is an amphoteric oxide which reacts with both strong acid and strong alkaline and cannot resist KOH etching. Prior to our research, lack of effective protection and safety methods was a dominating obstacle surrounding the use of this functional material. In fact, few reports presented cantilever sensors with ZnO and the protection methods. For example, Zhou et al. [6] theoretically designed and simulated a piezoelectric ZnO microcantilever chemical sensor, but they did not put it into practice. Itoh and Suga [7] successfully micromachined a force-sensing microcantilever with ZnO layers; however, they did not reveal the protection means in the KOH etching. Sudhir and Atul [8] have developed a physical protection method using mechanical jig, however this method is quite complex and needs many parts such as screw, plate, pipe, nut, Teflon, silicone O-ring, and neoprene gasket.

Fortunately, we have developed a novel, simple, and practical method to protect the ZnO film from alkaline etching with a protective coating of black wax (Apiezon-W). Hence, the selected piezoelectric layer in this study is a 𝑐-axis-oriented ZnO film.

The sensitivity of resonant microcantilever sensors is directly proportional to the resonant frequency [9]. The resonant frequency is a key parameter to design a sensor with a good sensitivity. Therefore, we put forward a simple and accurate formula to calculate the fundamental resonant frequency of T-shaped cantilevers using Rayleigh-Ritz method. We find that T-shaped cantilevers are superior to rectangular cantilevers, because with the same dimensions and same materials, T-shaped cantilevers can lead to higher fundamental resonant frequency and higher sensitivity. We are the first to report this useful formula, and we also validate the formula by simulation results and experimental results.

As shown in Figure 1, we have designed a novel piezoelectric ZnO cantilever sensor with a T-shaped geometry in order to enhance the fundamental resonant frequency and the sensitivity. The length and width of the cantilever beam are 288 μm and 108 μm. Besides, the dimensions of the cantilever extension are 96 μm long and 36 μm wide. The thicknesses of Si₃N₄ and ZnO film are 0.5 μm and 2 μm, respectively. The frequency characterization of the cantilever sensor has been accomplished by measuring the 𝑆₁₂ parameter using a network analyzer (Agilent E5100A).

(a) Slide view

(b) Top view

Figure 1 

Schematic drawing of the sensor.

2. Theoretical Analysis

2.1. Deflection Function of Rectangular Cantilevers

Figure 2 shows the structure of a single-layered or multilayered rectangular cantilever with length 𝐿, width 𝑊, equivalent thickness 𝐻, equivalent density 𝜌, and equivalent Young’s modulus 𝐸.

Figure 2 

Schematic drawing of a rectangular cantilever.

When applying a normal force 𝐹 at the free end of the cantilever, the second-order differential equation of the cantilever can be expressed as [10] 𝑑²𝑧(𝑥)𝑑𝑥²=𝐹(𝐿−𝑥)=()𝐸𝐼12𝐹𝐿−𝑥𝐸𝑊𝐻³, (1) where 𝑥 is the distance from the fixed end, and 𝐼=𝑊𝐻³/12 is the cross-sectional area moment of inertia.

As one end of the cantilever is fixed, the corresponding boundary conditions are 𝑧(0)=0,𝑑𝑧(𝑥)𝑑𝑥_𝑥=0=0. (2)(3)

The solution of (1)–(3) can be expressed as 𝑧(𝑥)=2𝐹𝑥²(3𝐿−𝑥)𝐸𝑊𝐻³=𝐴𝑥²(3𝐿−𝑥). (4)

This is the deflection function along the length direction, where 𝐴 is a constant.

2.2. Fundamental Resonant Frequency of T-Shaped Cantilevers

In this section, we derive the fundamental resonant frequency of T-shaped cantilevers using Rayleigh-Ritz method.

Figure 3 shows a typical T-shaped cantilever, whose dimension is defined by five parameters: 𝐿₀, 𝐿₁, 𝑊₀, 𝑊₁, and 𝐻. Obviously, the width function 𝑊(𝑥) of the T-shaped cantilever is a piecewise function that can be written as 𝑊(𝑥)=𝑊₁,𝑥∈0,𝐿₀𝑊₀,𝑥∈𝐿₀,𝐿₁. (5)

Figure 3 

Schematic drawing of a T-shaped cantilever.

The deflection function of (4) can be used as the mode shape, and the vibration displacement at each position can be written as 𝑧(𝑥,𝑡)=𝐴𝑥²3𝐿₁−𝑥sin2𝜋𝑓𝑡+𝛼, (6) where 𝐴 and 𝛼 are constants, 𝑡 is the time, and 𝑓 is the frequency.

The kinetic energy of the system is 𝑇=^𝐿1₀12𝜌𝐻𝑊(𝑥)𝑑𝑥𝜕𝑧𝜕𝑡²=2𝜋²𝑓²𝐴²𝜌𝐻cos²2𝜋𝑓𝑡+𝛼^𝐿1₀𝑊(𝑥)𝑥⁴3𝐿₁−𝑥²𝑑𝑥. (7)

Therefore, the maximum kinetic energy of the system is 𝑇_max=2𝜋²𝑓²𝐴²𝜌𝐻^𝐿1₀𝑊(𝑥)𝑥⁴3𝐿₁−𝑥²𝑑𝑥. (8)

The potential energy of the system is 𝑉=^𝐿1₀12(𝑥)𝜕𝐸𝐼²𝑧𝜕𝑥²²=3𝑑𝑥2𝐸𝐻³𝐴²sin²2𝜋𝑓𝑡+𝛼^𝐿1₀𝑊(𝑥)𝐿₁−𝑥²𝑑𝑥, (9) where 𝐼(𝑥)=𝑊(𝑥)𝐻³/12 is the cross-sectional area moment of inertia.

Therefore, the maximum potential energy of the system is 𝑉_max=32𝐸𝐻³𝐴^2𝐿1₀𝑊(𝑥)𝐿₁−𝑥²𝑑𝑥. (10)

According to conservation law of mechanical energy, the maximum kinetic energy equals to the maximum potential energy: 𝑇_max=𝑉_max. (11)

For calculation convenience, it is reasonable to define the width ratio 𝑝 and the length ratio 𝑞, both of which range from 0 to 1: 𝑊𝑝=⁰𝑊₁𝐿,𝑞=⁰𝐿₁𝑝∈[0,1],𝑞∈[0,1]. (12)

Hence, the fundamental resonant frequency can be obtained by substituting (8), (10), and (12) into (11): 𝑓=3𝐸𝐻³/4𝜋²∫^𝐿1₀𝑊(𝑥)𝐿₁−𝑥²𝑑𝑥𝜌𝐻∫^𝐿1₀𝑊(𝑥)𝑥⁴3𝐿₁−𝑥²=𝑑𝑥35𝐸𝜌𝐻2𝜋𝑊₁𝐿³₀−3𝐿₁𝑊₁𝐿²₀+3𝐿²₁𝑊₁𝐿₀+𝑊₀𝐿³₁−𝑊₀𝐿³₀+3𝐿₁𝑊₀𝐿²₀−3𝐿²₁𝑊₀𝐿₀5𝑊₁𝐿⁷₀−35𝐿₁𝑊₁𝐿⁶₀+63𝐿²₁𝑊₁𝐿⁵₀+33𝑊₀𝐿⁷₁−5𝑊₀𝐿⁷₀+35𝐿₁𝑊₀𝐿⁶₀−63𝐿²₁𝑊₀𝐿⁵₀=35𝐸𝜌𝐻2𝜋𝐿²₁𝑞³−3𝑞²+3𝑞+𝑝−𝑝𝑞³+3𝑝𝑞²−3𝑝𝑞5𝑞⁷−35𝑞⁶+63𝑞⁵+33𝑝−5𝑝𝑞⁷+35𝑝𝑞⁶−63𝑝𝑞⁵. (13)

In order to represent the relationship between the fundamental resonant frequency and the two ratios 𝑝 and 𝑞, we can define a dimensionless characteristic function: 𝑔𝑝,𝑞=𝑞³−3𝑞²+3𝑞+𝑝−𝑝𝑞³+3𝑝𝑞²−3𝑝𝑞5𝑞⁷−35𝑞⁶+63𝑞⁵+33𝑝−5𝑝𝑞⁷+35𝑝𝑞⁶−63𝑝𝑞⁵. (14)

Thus, the fundamental resonant frequency of T-shaped cantilever sensor can be written as 𝑓=35𝐸𝜌𝐻2𝜋𝐿²₁𝑔𝑝,𝑞. (15)

Figure 4 is the function image of 𝑔(𝑝,𝑞). 𝑔(𝑝,𝑞)>𝑔(1,𝑞) shows that, comparing to a rectangular cantilever with same dimensions and same materials, T-shaped cantilevers can always lead to higher fundamental resonant frequency and higher sensitivity. We also find that, when 𝑝 is fixed, the maximum value of 𝑔(𝑝,𝑞) can be obtained when 𝑞 reaches a proper value between 0 and 1.

Figure 4 

The function image of 𝑔(𝑝,𝑞).

Consider an n-layered T-shaped cantilever of density 𝜌_𝑖, Young’s modulus 𝐸_𝑖, and thickness 𝐻_𝑖 for 𝑖th (𝑖=1,2,3,…,𝑛) layer, as shown in Figure 5. We put forward an equivalent model method in which the three equivalent physical quantities are defined as follows.

Figure 5 

An n-layered T-shaped cantilever and its equivalent monolayered T-shaped cantilever.

Equivalent density: 𝜌_equ=∑^𝑛_𝑖=1𝜌_𝑖𝐻_𝑖∑^𝑛_𝑖=1𝐻_𝑖, (16)

Equivalent Young’s modulus: 𝐸_equ=∑^𝑛_𝑖=1𝐸_𝑖𝐻_𝑖∑^𝑛_𝑖=1𝐻_𝑖, (17)

Equivalent thickness: 𝐻_equ=^𝑛_𝑖=1𝐻_𝑖. (18)

With (16)–(18), the n-layered T-shaped cantilever can be treated as an equivalent monolayered T-shaped cantilever, whose fundamental resonant frequency is simply calculated by substituting these three equivalent parameters into (15) to get 𝑓=35𝐸_equ𝜌_equ𝐻_equ2𝜋𝐿²₁𝑔=𝑝,𝑞35∑^𝑛_𝑖=1𝐸_𝑖𝐻_𝑖∑^𝑛_𝑖=1𝜌_𝑖𝐻_𝑖∑^𝑛_𝑖=1𝐻_𝑖2𝜋𝐿²₁𝑔𝑝,𝑞. (19)

In order to validate (19), we have designed and fabricated a T-shaped piezoelectric ZnO cantilever sensor as shown in Figure 1. The cantilever sensor has a zinc oxide (ZnO) piezoelectric thin film between two Cr/Au layers on a supporting layer of Si₃N₄. The length and width of the cantilever beam are 288 μm and 108 μm. Besides, the dimensions of the cantilever extension are 96 μm long and 36 μm wide. The thicknesses of Si₃N₄ and ZnO film are 0.5 μm and 2 μm, respectively. The Cr/Au layers of 10 nm/50 nm are evaporated as the bottom electrode and top electrode. As the thicknesses of Cr/Au layers are much smaller than those of Si₃N₄ and ZnO film, the Cr/Au layers can be neglected when calculating the resonant frequency. Hence, the T-shaped piezoelectric ZnO cantilever can be treated as a double-layered T-shaped cantilever whose geometric and material data of each layer are given in Table 1.

Table 1 

Geometric and material data of the T-shaped piezoelectric ZnO cantilever.

Hence, the necessary parameters are listed below: 𝜌₁=5676Kg/m³,𝜌₂=3170Kg/m³,𝐸₁𝐸=209.7GPa,₂𝐻=270GPa,₁𝐻=2𝜇m,₂𝐿=0.5𝜇m,₀𝐿=288𝜇m,₁𝑊=288+96=384𝜇m,₀𝑊=36𝜇m,₁𝑊=108𝜇m,𝑝=⁰𝑊₁=13,𝐿𝑞=⁰𝐿₁=34. (20)

Substituting these parameters into (19), we get 𝑓=25.02kHz.

In order to assess the accuracy of (19), relative error 𝛿 is introduced to compare the calculation results with the corresponding experimental results or simulation results: 𝛿=𝑓−𝑓^′𝑓^′, (21) where 𝑓 refers to the result obtained by (19), and 𝑓^′ refers to the resonant frequency obtained by experiments or simulations.

According to experimental results discussed in Section 4, the resonant frequency of this device is 𝑓′=24.60kHz. Hence the relative error is 𝛿=25.02kHz−24.60kHz24.60kHz=1.71%. (22)

On the other hand, according to the finite-element method (FEM) simulation results, the resonant frequency of this device is 𝑓′=24.95kHz. The deformed shape of the first vibration mode is plotted in Figure 6. Hence the relative error is 𝛿=25.02kHz−24.95kHz24.95kHz=0.28%. (23)

Figure 6 

Deformed shape of the first vibration mode.

It can be noted from these statistics that the relative error is very small, and the formula we have deduced is reasonably accurate.

3. Fabrication Process

The piezoelectric ZnO cantilever sensor is fabricated by MEMS technique depicted in Figure 7. (a) Silicon with (100) orientation is used as a substrate, and 0.5 μm thick Si₃N₄ is deposited by LPCVD on both sides of a 510 μm thick silicon wafer. (b) The Si₃N₄ layers on front side and back side are respectively etched by RIE to form the cantilever shapes and the KOH etching windows. (c) An Cr/Au layer of 10 nm/50 nm used as bottom electrode is evaporated and patterned by lift off. (d) A 2 μm thick piezoelectric ZnO film is deposited by RF magnetron sputtering at 200°C, using a 99.999% pure Zn target. The sputtering gas is a mixture of 37.5% Ar and 62.5% O₂ at a pressure of 3 × 10⁻⁴Pa. (e) Another Cr/Au layer of 10 nm/50 nm used as top electrode is evaporated and patterned by lift off. Then, the ZnO film covering the bottom electrode is etched by dipping with hydrochloric acid. (f) The top of the device is protected by a thick coat of black wax (Apiezon-W), which can resist KOH etching. (g) The silicon is etched using 33 wt.% KOH solution at 75°C, below 80°C which is the softening point of Apiezon-W. (h) The Apiezon-W layer is finally removed by immerging into 1,1,1-trichloroethane.

Figure 7 

Fabrication processes of the sensor.

It is important to emphasize the difficulty for MEMS researchers to find a way to protect electric circuits and other delicate devices during deep silicon wet-etch processes. The challenge exists in choosing an appropriate protective coating that could meet these criteria: (1) easy to cover and remove, (2) having superior adhesion to the substrate without destroying the delicate devices below, (3) being able to persist KOH etchant for enough time. After testing a great many kinds of protective coatings, such as Cu and Crystalbond 509, we conclude that Apiezon-W is a novel and ideal choice, which is easy to operate and has strong protective capability.

4. Results and Discussion

Figure 8 is the cross-section SEM image of the 2 μm thick ZnO film. This figure shows that the ZnO columnar grains are clear and vertical to the substrate with a slight angle, indicating that the ZnO grains have good orientation. The 𝑐-axis orientation of the ZnO film is one of the most important factors of piezoelectric property, and the X-ray diffraction (XRD) pattern is used to investigate the 𝑐-axis properties. Figure 9 is the XRD pattern of the ZnO film with preferred (002) 𝑐-axis orientation. Figure 10 is the eventually fabricated piezoelectric ZnO cantilever sensor, which illustrates that the ZnO film is protected very well.

Figure 8 

SEM image of the cross-section of the ZnO film.

Figure 9 

XRD pattern of the ZnO film on Au.

Figure 10 

Fabricated piezoelectric ZnO cantilever.

The fundamental resonant frequency of the piezoelectric ZnO cantilever sensor is measured by an Agilent E5100A network analyzer. From the frequency response curve shown in Figure 11, we can find that the fundamental resonant frequency of this piezoelectric ZnO cantilever sensor occurs at 24.60 kHz, very close to the calculation results and simulation results.

Figure 11 

Frequency response of the piezoelectric ZnO cantilever sensor (𝑆12 parameter).

5. Conclusions

Using Rayleigh-Ritz method, the fundamental resonant frequency formula of T-shaped cantilevers is deduced for the first time, is validated by simulation results and experimental results, and can be widely used in design and optimization of T-shaped cantilevers. This formula illustrates that, comparing T-shaped cantilevers and rectangular cantilevers with the same dimensions and same materials, the former can lead to higher sensitivity. Then, a novel T-shaped piezoelectric ZnO cantilever sensor is designed and successfully fabricated by MEMS technique and finally tested by a network analyzer. The key step is protecting the ZnO film from KOH etching with a protective coating of black wax (Apiezon-W). This is one important technique that has shown considerable success. With this technique, many other delicate functional materials such as special ceramics, metals, polymers, and organic molecules will come into the use in the MEMS field. Experimental results show that this novel piezoelectric ZnO cantilever sensor has excellent dynamic response and can provide a new platform for chem/bio-sensing.