Electric Field Stiffening Effect in c-Oriented Aluminum Nitride

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Electric Field Stiffening Effect in C-Oriented Aluminum Nitride Piezoelectric Thin Film Cong Chen, Zhengguo Shang, Jia Gong, Feng Zhang, Hong Zhou, Bin Tang, Yi Xu, Chi Zhang, Ya Yang, and Xiaojing Mu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b14759 • Publication Date (Web): 20 Dec 2017 Downloaded from http://pubs.acs.org on December 20, 2017

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ACS Applied Materials & Interfaces

Electric Field Stiffening Effect in C-Oriented Aluminum Nitride Piezoelectric Thin Film Cong Chen,1,3 Zhengguo Shang,1,3 Jia Gong,1,3 Feng Zhang,1,3 Hong Zhou,1,3 Bin Tang,4 Yi Xu,1,3 Chi Zhang,2 Ya Yang,2* and Xiaojing Mu1,3* 1

Key Laboratory of Optoelectronic Technology & Systems, Ministry of Education, Chongqing

University, Chongqing 400044, P.R. China 2

Beijing Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing

100083, P.R. China 3

International R & D center of Micro-nano Systems and New Materials Technology, Chongqing

University, Chongqing 400044, P.R. China 4

Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900,

Sichuan, P.R. China * Corresponding author Email: [email protected] and [email protected] KEYWORDS: stiffness modulation, electric field bias, piezoelectric thin film, aluminum nitride, film bulk acoustic resonator, atomic interaction

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ABSTRACT

Aluminum nitride offers unique material advantages for the realization of ultra-high frequency acoustic devices due to its high ratio of stiffness to density, compatibility with harsh environments and superior thermal properties. Although to date aluminum nitride thin film has been widely investigated in electrical and mechanical characteristics under alternating small signal excitation, its ultrathin nature under large bias may also provide novel and useful properties. Here we present a comprehensive investigation of electric field stiffening effect in coriented aluminum nitride piezoelectric thin film. By analyzing resonance characteristic in a 2.5GHz aluminum nitride based film bulk acoustic resonator, we demonstrate an up to 10% linear variation in equivalent stiffness of aluminum nitride piezoelectric thin film when applied an electric field from -150MV/m to +150MV/m along c-axis. Moreover, for the first time, an atomic interaction mechanism is proposed to reveal the nature of electric field stiffening effect, suggesting the nonlinear variation of the interatomic force induced by electric field modulation is the intrinsic reason for this phenomenon in aluminum nitride piezoelectric thin film. Our work provides vital experimental data and effective theoretical foundation for electric field stiffening effect in aluminum nitride piezoelectric thin film, indicating huge potential in tunable ultra-high frequency microwave devices.

Wurtzite materials including aluminum nitride, zinc oxide, cadmium sulfide, gallium nitride, and indium nitride are envisioned as fundamental building blocks of future electronic, electromechanical, optoelectronic nano-devices and nano-systems.1,2 Among aforementioned materials, aluminum nitride (AlN) thin film has been proved to be a promising material for electronic applications due to the combination of electrical,3 thermal,4 acoustic,5 piezoelectric6


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and photoelectrical7 properties. In particular, it is the ideal material for radio frequency (RF) acoustic devices for its outstanding performance, including high acoustic velocity, low loss, high thermal conductivity, low dielectric constant, low linear thermal expansion coefficient and complementary metal-oxide semiconductor (CMOS) integration compatibility.8-10 A variety of applications have been implemented in this area, such as AlN based resonators,11,12 filters,13,14 oscillators15,16 and resonant sensors.17-21 It is well known that AlN based RF acoustic wave devices mainly utilize the resonance characteristic of this material, which is closely related to the equivalent stiffness coefficient of the material. On the other hand, stiffening effect can be induced in AlN thin film under an electric field bias, which leads to a changed equivalent stiffness of the AlN film resulting in the shift of the resonance frequency.22,23 From this perspective, electric field stiffening effect provides a promising route to realize frequency tunable AlN based microwave devices, which has tremendous application value and broad prospect. In particular, among all types of tunable technologies, the one based on electric field stiffening mechanism offers distinctive advantages over other approaches, since it enables tunability and resonance to coexist in one single piezoelectric thin film in contrast with traditional technologies, which typically need extra frequency control unit, such as tunable capacitor24 or adjustable microheater.25 To date, research on electric field stiffening effect of AlN thin film is still rare. Although several studies have been done to investigate the relationship between equivalent stiffness coefficient and bias electric field,26,27 it still remains blank in the mechanism of such phenomena. Besides, sizable difference also appeared in the results of previous studies. This is attributed to the use of AlN based solid mounted resonator (SMR) which is a kind of multilayer composite


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structure, leading to the increment of roughness and mechanical loss in AlN thin film and finally give rise to deviation in the process of extraction of equivalent stiffness. In this paper, enabled by analyzing resonance characteristic in a 2.5 GHz direct current (DC) voltage biased electromechanical thin film bulk acoustic resonator instead of solid mounted resonator, we reveal strong electric field stiffening effect in c-oriented AlN piezoelectric thin film. Furthermore, a theoretical model on the atomic scale involving in the interaction force between atoms is also proposed to explain the electric field stiffening effect for the first time, which is in good agreement with the experimental data. Our work provides both experimental data and theoretical basis to realize wide range frequency-tunable AlN based microwave devices at ultra-high frequencies without extra frequency control unit, indicating a significant step toward RF applications. RESULTS AND DISCUSSION Approach Description. Currently, for characterizing mechanical properties in nano-scale materials, the most common method is nanoindentation.28,29 Nevertheless, this method may seem impractical to implement on AlN piezoelectric thin film with direct current bias. Because it’s hard for indenter to contact the surface of AlN thin film, which is sandwiched between top and bottom electrodes used to generate longitudinal electric field bias. Thanks to the piezoelectric transduction properties of the AlN thin film, it enables us to measure and analyze the mechanical properties via electromechanical resonance method,30 which is perfectly compatible with the bias electric field. First we need to design and fabricate an AlN based film bulk acoustic resonator. Then measure the electromechanical resonance frequency at different bias electric fields. Finally utilizing equivalent electromechanical model, we can extract equivalent stiffness coefficient of


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AlN from the measured resonance frequency. This is our approach to acquiring quantification result of the electric field stiffening effect in c-oriented AlN piezoelectric thin film. Device Design, Fabrication and Characterization. The designed piezoelectric film bulk acoustic resonator, illustrated in Figure 1, is composed of five thin films grown on silicon (Si) substrate (300-um thick). The top layer (aluminum (Al)) is patterned to form a pentagonal upper electrode and an electrical connection strip used to conduct electrical signals to pad (S) from the upper electrode. The piezoelectric layer (c-oriented AlN) covers the whole area except two etched vias accessing to connection strip of the bottom electrode. The following two layers (platinum (Pt) and titanium (Ti) respectively) are patterned simultaneously to form mirror symmetrical pentagonal bottom electrode with corresponding connection strip. The bottom is an entire layer of silicon dioxide (SiO2) used to act as a supporting diaphragm and also provide electrical insulation between the bottom electrode and substrate material. Finally the whole structure is released from the backside of Si substrate to the SiO2 layer to create a cavity underneath the pentagonal electrodes.


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Figure 1. AlN based film bulk acoustic resonator. (a) Explosive view of layered structure of the designed resonator. (b) Schematic of measuring principle. The resonator is excited by applying a RF signal between the top and bottom electrodes. Meanwhile a DC voltage is superimposed on the RF signal to generate a bias electric field along the thickness direction of the piezoelectric thin film. Due to the electric field dependence of equivalent stiffness of AlN thin film, the resonance frequency of the resonator shifts from f0 to f0+△f. (c) Optical electron microscope (OEM) of fabricated resonator from backside view. The overlapped electrodes are designed to be pentagonal to ensure better resonance performance. (d) Scanning electron microscope (SEM) of the cross-sectional view of the layered resonator. The thickness of each layer is as follows: d1=195 nm; d2=598 nm; d3=125 nm; d4=37 nm; d5=542 nm.

When a RF signal is applied between the two electrodes of the resonator, an alternating electric field along the thickness direction will be generated in piezoelectric layer. And the thickness extension vibration mode is excited through e33 piezoelectric coefficient of AlN when the frequency of the RF signal coincides with the natural resonance frequency, f0, of the


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resonator. Here, f0 depends on the mechanical parameters and geometric dimension of each layer of the resonator, including stiffness, density and film thickness. If a DC bias electric field is imposed on the AlN piezoelectric thin film, polar atoms in the lattice drift away their equilibrium positions due to the effect of electrostatic force, leading to a change of equivalent stiffness of coriented AlN thin film. Such electric field induced stiffness variation eventually results in a shift in the resonance frequency of the resonator (from f0 to f0+△f). Therefore, the electric field stiffening effect can be readily detected and investigated by monitoring the resonance frequency of the proposed electromechanical resonator. On the basis of this design, the proposed AlN based film bulk acoustic resonator was fabricated utilizing a complementary metal-oxide-semiconductor (CMOS) compatible microfabrication process involving a combination of five masks photolithography (See Methods). The admittance curve near the resonance frequency and corresponding vibration mode are depicted in Figure 2(a) showing an electromechanical resonance frequency of around 2.5GHz. Obvious frequency shifts in the designed resonator were observed under different bias electric fields, as shown in Figure 2(b) and 2(c). Both resonance frequency fr and anti-resonance frequency fa collected in Figure 2(d) exhibit the same trends with bias electric field, which increase linearly with the increment of bias electric field in the whole test range indicating stiffness variation is the prominent reason for frequencies variations. We do note that the admittance curves in the vicinity of the resonance frequency are relatively flat compared to that of anti-resonance frequency, which is attributed to the presence of a large resistance of electrical connection strip connected to electrodes and pads, which has no influence on resonance frequency.


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Figure 2. Experimental results. (a) Measured admittance curve versus frequency at various bias electric fields. The inset shows simulated mechanical deformation of the profile, indicating a thickness extension mode is excited in the film bulk acoustic resonator. (b) and (c) are the enlarged views of the admittance curve near the resonance frequencies (corresponding to the maximum points of admittance curve) and anti-resonance frequencies (corresponding to the minimum points), respectively. (d) Resonance frequency and anti-resonance frequency as a function of bias electric field. Both the resonance frequency and anti-resonance frequency experience a similar variation of 14MHz and 10MHz respectively with the increasing bias electric field from 150MV/m to 150MV/m.

Extraction for Equivalent Stiffness. As we have shown, electric field induced equivalent stiffness variation will finally result in frequency shift in AlN based thickness extension mode resonator. In order to capture the quantitative relationship between equivalent stiffness and bias electric field, we established electromechanical equivalent model of the thin film bulk acoustic resonator (specific derivation process presented in Supporting Information), as shown in Figure 3.


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Figure 3. Equivalent electromechanical model for five-layer film bulk acoustic resonator. The parameters am and bm (m=1,2,3,4,5) represent acoustic impedance of each layer related to acoustic parameters and geometric dimensions of corresponding layer.

According to transmission line theory, the admittance expression of the resonator can be derived as

Y=

M 22 M 12

(1)

where M22 is the element in the second row and second column of the matrix M, M12 is the element in the first row and second column of the matrix M. Here, M is a second order matrix given by

 1 0  1 i ωC0  1 n 0  M =    M 1，2 M 3 M 4 M 5 iωC0 1  0 1   0 n 

(2)

where C0 is the static capacitance of the resonator, n is the electromechanical conversion factor. Besides M1,2 is the equivalent transmission matrix for Al top electrode and AlN piezoelectric layer, M3, M4 and M5 are the transmission matrixes for Pt bottom electrode, Ti seed layer and SiO2 supporting layer, respectively, given by


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M 1,2

b2  +1  a1b1 a + a +  1 2 a1 + b1 =  1   a1 + a2 + a1b1  a1 + b1

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 + a2 + b2  ab a1 + a2 + 1 1  a1 + b1   a2 +1  ab  a1 + a2 + 1 1  a1 + b1 b2 a2

 ak ak2  + 1 2 a + k   bk bk   Mk =  1  ak +1   bk  bk 

,

(3)

k = 3, 4,5

(4)

  km d m  am = i ρ m vm S tan  2      ρ m vm S , m = 1, 2,3, 4,5 bm = i sin ( k d ) m m  vm = cm ρ m  km = ω v m = 2π f vm

(5)

where the subscripts ‘1’, ‘2’, ‘3’, ‘4’, ‘5’ denote Al, AlN, Pt, Ti and SiO2 respectively, cm is the Young's modulus of corresponding material, ρm is the density of material, dm is the thickness of each layer, S is the overlapped area between the bottom electrode and the top electrode. All the material parameters used to calculate the theoretical admittance curve are listed in Table 1, in which X represents the equivalent stiffness of AlN that needs to be extracted. Table 1. Material parameters used for extraction. cD33/c11

ρ

d

e33

εx33

S

GPa

kg/m2

nm

C/m2

F/m

µm2

Al

70

2700

195

---

---

1.72×1202

AlN

X

3260

598

1.55

9.7×10-11

---


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Pt

168

21450

125

---

---

1.72×1202

Ti

115.7

4506

37

---

---

1.72×1202

SiO2

70

2200

542

---

---

---

Then an algorithm based on iteration method (see Supporting Information, Figure S4) was used to extract the value of equivalent stiffness from the obtained anti-resonance frequency at different bias electric fields. The extracted equivalent stiffness versus bias electric field is depicted in Figure 4. The result shows that with the increasing of electric field, the value of equivalent stiffness in c-oriented AlN thin film keeps increasing linearly. An up to 10% relative change of equivalent stiffness was observed from -150MV/m to 150MV/m, indicating a sensitivity of 333ppm/(MV/m).

Figure 4. Extracted equivalent stiffness versus electric field. Inset: Displacement deformation of AlN piezoelectric thin film under bias electric field in different directions.

Mechanism. According to the theory of piezoelectricity,31 the equivalent stiffness of AlN is composed of two parts, given by c33D = c33E + e332 ε 33x

(6)

where c E33 , e33 and ɛ x33 are the Young's modulus along c-axis at a constant electric field, piezoelectric stress coefficients and dielectric permittivity at constant strain, respectively. The


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equivalent stiffness c D33 depends on an applied bias electric field in the material through the dependences of both cE33 and e233/ɛx33 these two parts on the bias electric field. Thanks to previous research, the relationship between e233/ɛx33 and bias electric field can be obtained,26 as depicted in Figure 5 (blue data). Removing this part e233/ɛx33 from cD33 extracted in Figure 4, we can obtain the dependency of Young's modulus on the bias electric field, as shown in Figure 5 (red data). It can be seen that with the increasing of bias electric field piezoelectric enhanced part e233/ɛx33 gradually decreases, which is contrary to the trend of cD33. That suggests the variation of equivalent stiffness induced by bias electric field is almost completely contributed by the dependency of Young's modulus on the bias electric field.

Figure 5. Young’s modulus and piezoelectric enhanced part versus electric field.

To further understand the electric field stiffening effect in Young's modulus of c-oriented AlN piezoelectric thin film, we turn to the crystal structure of such material. From the microscopic perspective, Young's modulus is a reflection of the bond strength between atoms. It is well known that AlN crystal possess hexagonal wurtzite structure. In such crystalline lattice structure, each Al (N) atom is surrounded by four N (Al) atoms, forming a distorted tetrahedron with three Al-N bonds named B1 and one Al-N bond in the direction of the c-axis, named B2, as illustrated in the inset of Figure 6. The bond B2 is formed by the coupling of the Al empty orbit and the N full orbit, resulting in greater ionic character in B2. Since the nitrogen nucleus has a


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stronger attraction force than that of aluminum nucleus in bond B2, the shared electrons will be biased towards nitrogen nucleus, which enables relatively negatively charged state of nitrogen atom and relatively positively charged state of aluminum atom respectively. According to BornLandé equation, both Coulomb force and Born force coexist in bond B2. The Coulomb force is an attractive force due to the opposite relatively charged states of the two atoms and is given by

F1 =k

q1 ⋅ q2 r2

rˆ

(7)

where k=8.988×109N·m2/C2 is the Coulomb constant, |q1|=|q2|=3e are the relative charge of the nitrogen atom and aluminum atom (e=1.602×10-19C is the electrostatic charge carried by an electron), r is the distance between nitrogen atom and aluminum atom, ȓ is the unit vector in the direction of attractive force. On the other hand, Born force is a repulsive force caused by electron-electron and nucleus-nucleus interactions and can be expressed as

F2 = − k

q1 ⋅ q2 ⋅ r0n −1

r n +1

rˆ

(8)

where r0=1.917×10-10m is the distance between nitrogen atom and aluminum atom at equilibrium positions (with no electric field), n=3 is the Born exponent. The join force between the two atoms is the vector sum of the Coulomb force and the Born force and can be calculated by

F = F1 + F2

(9)

All the three forces are illustrated in Figure 6. At the micro scale, Young's modulus of c-oriented AlN crystal can be defined by the amplitude of the join force F and distance r between nitrogen atom and aluminum atom in bond B2, given by YM = α ⋅ dF dr , where α is a constant. It is worth


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noting that dF/dr is rightly the slope of the join force curve, which indicates that a steeper slope will result in a greater Young's modulus.

Figure 6. Interaction force between aluminum atom and nitrogen atom in bond B2. Inset: Modulation of positive and negative electric field on bond B2, respectively.

In bond B2 with no bias electric field, the join force is zero, suggesting the nitrogen atom and the aluminum atom are kept in their own equilibrium positions where attractive and repulsive forces are exactly equal. When an electric field is applied along the c-axis direction, the nitrogen atom and aluminum atom will deviate from respective equilibrium positions due to the effect of electrostatic forces. To be specific, for positive (c-axis positive direction) electric field E1, relatively negatively charged nitrogen atom moves towards c-axis negative direction while

positively charged aluminum atom moves inversely, leading to a decreased distance r1 between two atoms, as shown in the inset of Figure 6. On the contrary, negative electric field E2 will result in an increased distance r2 between two atoms. From the join force curve, it can be clearly seen that the slope k1 corresponding to distance r1 is steeper than k2 corresponding to distance r2, suggesting Young's modulus at E1 is larger than that at E2. Furthermore, it is important to note that near the equilibrium position (r=r0) the slope of join force curve shows monotonic decreasing characteristic, which coincide well with the variation trend of extracted Young’s


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modulus at different electric fields. Based on the above analysis, it can be seen that the nature of electric field stiffening effect is the nonlinear variation of the interatomic force induced by electric field modulation. Quantitative Analysis of Electric Field Stiffening Effect. Considering Born exponent n=3, thus the amplitude of the join force F can be derived by

F = F1 ⋅ rˆ + F2 ⋅ rˆ =k ⋅ q1 ⋅ q2 ⋅ (

1 r02 − ) r2 r4

(10)

Then the Young's modulus can be expressed by

YM = α ⋅ dF dr = α k ⋅ q1 ⋅ q2 ⋅ (−

2 4r02 ) + r3 r5

(11)

When applying a DC electric filed, the thickness of AlN piezoelectric thin film will get stretched or compressed due to inverse piezoelectric effect. And the change in thickness can be obtained by[26] e ∆t = E33=0 ⋅ E t0 c33

(12)

where ∆t is the absolute change in thickness, t0 is the thickness of AlN at E=0. Thus the relationship between the chemical bond length and external electric field can be estimated by r ( E ) − r0 ∆r ∆t = ≈ r0 r0 t0


(13)

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where ∆r is the absolute change in chemical bond length, r0 is the chemical bond length at E=0, r(E) is the chemical bond length at certain electric field. Substituting Equation (13) into (12), we

can obtain the relationship by

  e r ( E ) = r0 1 + E33=0 ⋅ E   c33 

(14)

Substituting Equation (14) into (11), we can obtain the relationship between Young's modulus and electric field by

    2 4   YM = α k ⋅ q1 ⋅ q2 ⋅  − + 3 5  r 3 1 + e33 ⋅ E  r 3  1 + e33 ⋅ E    0  E =0  0  c33E = 0   c33  

(15)

This equation is the final expression about Young's modulus modulated by electric field. As mentioned in the previous section, k=8.988×109N·m2/C2, |q1|=|q2|=3e, e=1.602×10-19C, r0=1.917×10-10m. The typical values for e33 can be obtained by[18] e33=-1.55 C/m2. According to

our extraction result, cE=0 33 =387.1GPa. For E=0, YM = c33E = 0

(16)

Solving Equation (16), we obtain α=6.568×108m-1. Considering all the parameters in Equation (15) are known, thus we can plot the curve about Young’s modulus change with respect to electric field, as shown in Figure 7.


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Figure 7. Young’s modulus with respect to electric field by theoretical model.

From Figure 7, it can be seen that Young's modulus increases linearly with applied electric field, which coincides well with the trend observed in our experimental result shown in Figure 5. Meanwhile, a mismatch in the modulation range is also noted. The date shows the theoretical modulation range is only one-tenth of that of experimental data. This deviation is mainly caused by the following reasons: (a) in our model, only one ion pair is considered to calculate the interaction force, in fact, the interaction force on each ionic atom is also contributed by other ionic atoms in the lattice; (b) during the estimation of B2 length with respect to electric field, we ignore the length variation in B1, which will weaken the variation in B2 length; (c) the Coulomb force and Born force based on Born-Landé equation that we use are established from classic physics perspective, which ignores quantum effect induced by electronic cloud in the chemical bond B2, thus there may be some problems in the process of precise calculation and prediction for the observed electric field stiffening effect. In the near future, we are going to address these problems and establish a more accurate model for precise prediction of such electric field stiffening effect. CONCLUSIONS


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In this article, we have systematically investigated electric field stiffening effect in coriented AlN piezoelectric thin film. We demonstrated efficient electric field induced modulation on equivalent stiffness of AlN, with up to 10% relatively variation in the range of (-150MV/m, 150MV/m). In addition, we found that the variation of equivalent stiffness is mainly contributed by the dependency of Young's modulus on the bias electric field. More importantly, an atomic interaction mechanism was first proposed to interpret the variation of Young's modulus induced by electric field, which shed light on the nature of electric field stiffening effect. Our work provides both experimental data and theoretical basis to realize wide range frequency-tunable AlN based microwave devices at ultra-high frequencies without extra frequency control unit, indicating a significant step toward RF applications. Besides the new understanding of electric field stiffening effect in AlN can also be extended to GaN, CdS, ZnO, and other wurtzite materials and therefore enable us to better study similar physical phenomena for specific applications. METHODS Device Fabrication. The proposed electromechanical resonator used to investigate electric field stiffening effect in AlN piezoelectric thin film was fabricated utilizing a five-mask micro fabrication process, shown in Figure 8. The process flow is as follows: (a) 542-nm-thick doublesided SiO2 layers were grown on a high-resistivity (20,000) 4-inch silicon wafer via thermal oxidation process; (b) 37-nm-thick Ti and 125-nm-thick Pt were sputter-deposited successively, followed by lift-off process to define the bottom electrode; (c) 598-nm-thick high-quality c-axis orientated AlN piezoelectric film was deposited on the Pt/Ti electrode by pulse DC reaction magnetron sputtering at room temperature; (d) 195-nm-thick Al was sputter-deposited and patterned by wet etching to form the top electrode; (e) vias were opened in AlN layer by wet


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etching in TMAH to get access to the bottom electrode; (f) 800-nm-thick Al was deposited by DC magnetron sputtering and patterned by wet etching to define the probing pad; (g) 2-um-thick photoresist (PR) was coated on the front side of the wafer via spin coater to protect Al top electrode from acidic etching used in the next process; (h) 100-nm-thick Al was sputterdeposited on the backside of the wafer and patterned in hydrofluoric acid (HF), which also etched adjacent SiO2 layer (here Al is used to provide an extra protection layer for bulk silicon which should not be etched during backside release process); (i) the foregoing photoresist on the front side of wafer was removed by acetone; (j) 300-µm-thick Si substrate underneath the SiO2 supporting layer was etched by sulfur hexafluoride (SF6) to completely release the device.

Figure 8. Microfabrication process for the electromechanical resonator. A-A’ and B-B’ denote longitudinal and transversal axis of the device, as illustrated in Figure 1(b). (a) SiO2 layers growth via thermal oxidation. (b) Ti/Pt layers sputter-deposition and patterning. (c) AlN piezoelectric film deposition by pulse DC reaction magnetron sputtering. (d) Al upper electrode deposition and patterning. (e) Vias forming by wet etching. (f)

Al pads deposition and patterning. (g) PR coating for protection. (h) Backside Al protection layer deposition and pattering. (i) Removing foregoing photoresist. (j) Backside release by DRIE.

AlN Characterization. In order to determine the crystal orientation of the as-grown AlN piezoelectric thin film, X-ray diffraction (XRD), which is widely used to characterize nano-, poly- and single- crystalline thin film, was performed on a freshly grown sample. The result


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shows that the (002) diffraction peak of the AlN thin film at 2θ=36° is at least ten times stronger than other peaks, which suggests AlN thin film possess wurtzite structure and grows in c-axis preferred orientation, as shown in Figure 9. Moreover, a full width at half maximum (FWHM) value of the AlN (002) orientation rocking curve is 1.995° obtained from the inset of Figure 9, which verifies the high quality of the c-oriented AlN piezoelectric thin film.

Figure 9. XRD pattern of the as-grown AlN piezoelectric thin film. The inset shows the rocking curve of the (002) orientation of the AlN thin film.

Experimental Setup. The resonant performance of the film bulk acoustic resonator was characterized by measuring its equivalent electrical admittance with a Keysight E5080A vector network analyzer connecting to a Cascade Microtech EPS150RF probe platform. After performing an open-short-load calibration on a standard substrate, the resonator was measured by an Infinity I40-GSG-250 probe. The scattering parameter S11 of this one-port resonator was first obtained and then converted into the admittance Y according to: Y=(1-S11)/(1+S11)/50. A DC voltage supplied by a Keysight E36106A was added to the RF signal from the VNA by a Keysight 11590B bias tee to generate an electric field along the thickness direction of the AlN piezoelectric thin film. The measurement bandwidth (IFBW) of the network analyzer was set to


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500Hz, which is small enough to obtain a good noise performance. All experiments were performed in an open environment in ambient temperature and pressure. The experiment is realized with the setup (see Supporting Information, Figure S5).

ASSOCIATED CONTENT Supporting Information The following files are available free of charge. Mathematical derivation for the electromechanical equivalent model of thin film bulk acoustic resonator, the flowchart for extraction of equivalent stiffness and the schematic of experimental setup (PDF) AUTHOR INFORMATION Corresponding Author *E-mail: [email protected], [email protected]. Present Addresses No. Shazheng St.174, Shapingba, Chongqing 400044 Cell Phone: +86 15902396712 Author Contributions Cong Chen, Prof. Xiaojing Mu and Prof. Ya Yang initiated the study and proposed the approach of the research. Prof. Xiaojing Mu, Prof. Chi Zhang and Prof. Yi Xu provided theory consultant and supervised the research. Cong Chen and Feng Zhang established the theory model and


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implemented finite element simulation. Cong Chen, Zhengguo Shang and Bin Tang prepared the devices including design, fabrication and characterization. Cong Chen, Hong Zhou and Jia Gong carried out the experiments. Cong Chen prepared the manuscript. All authors revised the manuscript. Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work is supported by the National Key Research and Development Program of China (Grant No.2016YFB0402702), National Natural Science Foundation of China (Grant No. 51605060),

the

Fundamental

Research

Funds

for

the

Central

Universities

(No.106112016CDJZR125504), Ministry of Education of the People's Republic of China, and the “thousands talents” program for the pioneer researcher and his innovation team, China. REFERENCES 1.

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10. Caliendo, C. Gigahertz-band Electroacoustic Devices Based on AlN Thick Films Sputtered on Al2O3 at Low Temperature. Appl. Phys. Lett. 2003, 83, 4851-4853. 11. Lin, C.; Chen, Y.; Felmetsger, V. V.; Senesky, D. G.; Pisano, A. P. AlN/3C–SiC Composite Plate Enabling High-frequency and High-Q Micromechanical Resonators. Adv. Mater. 2012, 24, 2722-2727.

12. Sun, C.; Soon, B. W.; Zhu, Y.; Wang, N.; Loke, S. P. H.; Mu, X.; Tao, J.; Gu, A. Y. Methods for Improving Electromechanical Coupling Coefficient in Two Dimensional


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Electric Field Excited AlN Lamb Wave Resonators. Appl. Phys. Lett. 2015, 106, 253502. 13. Kim, B.; Olsson, R. H.; Wojciechowski, K. E. AlN Microresonator-based Filters with Multiple Bandwidths at Low Intermediate Frequencies. J. Microelectromech. S. 2013, 22, 949-961. 14. Zuo, C.; Sinha, N.; Piazza, G. Very High Frequency Channel-select MEMS Filters Based on Self-coupled Piezoelectric AlN Contour-mode Resonators. Sens. Actuators, A 2010, 160, 132-140. 15. Wojciechowski, K. E.; Baker, M. S.; Clews, P. J.; Olsson, R. H. A Fully Integrated Oven Controlled Microelectromechanical Oscillator—part I: Design and Fabrication. J. Microelectromech. S. 2015, 24, 1782-1794.

16. Zuo, C.; Spiegel, J. V. D.; Piazza, G. Dual-mode Resonator and Switchless Reconfigurable Oscillator Based on Piezoelectric AlN MEMS Technology. IEEE T. Electron Dev. 2011, 58, 3599-3603. 17. Hui, Y.; Gomez-diaz, J. S.; Qian, Z. Y.; Alù, A.; Rinaldi, M. Plasmonic Piezoelectric Nanomechanical Resonator for Spectrally Selective Infrared Sensing. Nat. Commun. 2016, 7, 11249.

18. Mu, X.; Kropelnicki, P.; Wang, Y.; Randles, A. B. Dual Mode Acoustic Wave Sensor for Precise Pressure Reading. Appl. Phys. Lett. 2014, 105, 113507. 19. Pang, W.; Zhao, H.; Kim, E. S.; Zhang, H.; Yu, H.; Hu, X. Piezoelectric Microelectromechanical Resonant Sensors for Chemical and Biological Detection. Lab Chip 2012, 12, 29-44. 20. Liu, W.; Wang, J.; Yu, Y.; Chang, Y.; Tang, N.; Qu, H.; Wang, Y.; Pang, W.; Zhang, H.; Zhang, D.; Xu, H.; Duan, X. Tuning the Resonant Frequency of Resonators Using Molecular


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Surface Self-assembly Approach. ACS Appl. Mater. Interfaces 2015, 7, 950−958. 21. Lu, Y.; Chang, Y.; Tang, N.; Qu, H.; Liu, J.; Pang, W.; Zhang, H.; Zhang, D.; Duan, X. Detection of Volatile Organic Compounds Using Microfabricated Resonator Array Functionalized with Supramolecular Monolayers. ACS Appl. Mater. Interfaces 2015, 7, 17893−17903. 22. Karabalin, R. B.; Matheny, M. H.; Feng, X. L.; Defay, E.; Rhun, G. L.; Marcoux, C.; Hentz, S.; Andreucci, P.; Roukes, M. L. Piezoelectric Nanoelectromechanical Resonators Based on Aluminum Nitride Thin Films. Appl. Phys. Lett. 2009, 95, 103111. 23. Nan, T.; Hui, Y.; Matteo, R.; Sun, N. X. Self-biased 215MHz Magnetoelectric NEMS Resonator for Ultra-sensitive DC Magnetic Field Detection. Sci. Rep. 2013, 3, 1985. 24. Pang, W.; Zhang, H.; Yu, H.; Lee, C. Y.; Kim, E. S. Electrical Frequency Tuning of Film Bulk Acoustic Resonator. J. Microelectromech. S. 2007, 16, 1303-1313. 25. Ruby, R.; Merchant, P. Micromachined Thin Film Bulk Acoustic Resonators. IEEE International Frequency Control Symposium 1994, 135-138.

26. Hemert, T. V.; Reimann, K.; Hueting, R. J. E. Extraction of Second Order Piezoelectric Parameters in Bulk Acoustic Wave Resonators. Appl. Phys. Lett. 2012, 100, 232901. 27. Defay, E.; Ben, H. N.; Emery, P.; Parat, G.; Abergel, J.; Devos, A. Tunability of Aluminum Nitride Acoustic Resonators: a Phenomenological Approach. IEEE T. Ultrason. Ferr. 2011, 58, 2516-2520.

28. Lee, C.; Wei, X.; Kysar, J. W.; Hone, J. Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. Science 2008, 321, 385-388. 29. Wang, Z.; Jia, H.; Zheng, X. Q.; Yang, R.; Ye, G. J.; Chen, X. H.; Feng P. X. Resolving and Tuning Mechanical Anisotropy in Black Phosphorus Via Nanomechanical Multimode


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Resonance Spectromicroscopy. Nano Lett. 2016, 16, 5394-5400. 30. Li, P.; Liao, Q.; Yang, S.; Bai, X.; Huang, Y.; Yan, X.; Zhang, Z.; Liu, S.; Lin, P.; Kang, Z.; Zhang, Y. In Situ Transmission Electron Microscopy Investigation on Fatigue Behavior of Single ZnO Wires under High-Cycle Strain. Nano Lett. 2014, 14, 480-485. 31. Peizoelectrically Active Acoustic Propagation. In Bulck Acoustic Wave Theory and Devices; Rosenbaum, J. F.; Artech House: Norwood, 1988; pp 143-145.

Table of Contents Graphic


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Figure 1. AlN based film bulk acoustic resonator. (a) Explosive view of layered structure of the designed resonator. (b) Schematic of measuring principle. The resonator is excited by applying a RF signal between the top and bottom electrodes. Meanwhile a DC voltage is superimposed on the RF signal to generate a bias electric field along the thickness direction of the piezoelectric thin film. Due to the electric field dependence of equivalent stiffness of AlN thin film, the resonance frequency of the resonator shifts from f0 to f0+△f. (c) Optical electron microscope (OEM) of fabricated resonator from backside view. The overlapped electrodes are designed to be pentagonal to ensure better resonance performance. (d) Scanning electron microscope (SEM) of the cross-sectional view of the layered resonator. The thickness of each layer is as follows: d1=195 nm; d2=598 nm; d3=125 nm; d4=37 nm; d5=542 nm. 115x95mm (300 x 300 DPI)



Figure 2. Experimental results. (a) Measured admittance curve versus frequency at various bias electric fields. The inset shows simulated mechanical deformation of the profile, indicating a thickness extension mode is excited in the film bulk acoustic resonator. (b) and (c) are the enlarged views of the admittance curve near the resonance frequencies (corresponding to the maximum points of admittance curve) and antiresonance frequencies (corresponding to the minimum points), respectively. (d) Resonance frequency and anti-resonance frequency as a function of bias electric field. Both the resonance frequency and antiresonance frequency experience a similar variation of 14MHz and 10MHz respectively with the increasing bias electric field from -150MV/m to 150MV/m. 94x63mm (300 x 300 DPI)


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Figure 3. Equivalent electromechanical model for five-layer film bulk acoustic resonator. The parameters am and bm (m=1,2,3,4,5) represent acoustic impedance of each layer related to acoustic parameters and geometric dimensions of corresponding layer. 46x15mm (300 x 300 DPI)



Figure 4. Extracted equivalent stiffness versus electric field. Inset: Simulated displacement profile of aluminum nitride piezoelectric thin film under bias electric field in different directions. 56x40mm (300 x 300 DPI)


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Figure 5. Young’s modulus and piezoelectric enhanced part versus electric field. 50x31mm (300 x 300 DPI)



Figure 6. Interaction force between aluminum atom and nitrogen atom in bond B2. Inset: Modulation of positive and negative electric field on bond B2, respectively. 56x39mm (300 x 300 DPI)


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Figure 7. Young’s modulus with respect to electric field by theoretical model. 235x164mm (300 x 300 DPI)



Figure 8. Microfabrication process for the electromechanical resonator. A-A’ and B-B’ denote longitudinal and transversal axis of the device, as illustrated in Figure 1(b). (a) SiO2 layers growth via thermal oxidation. (b) Ti/Pt layers sputter-deposition and patterning. (c) AlN piezoelectric film deposition by pulse DC reaction magnetron sputtering. (d) Al upper electrode deposition and patterning. (e) Vias forming by wet etching. (f) Al pads deposition and patterning. (g) PR coating for protection. (h) Backside Al protection layer deposition and pattering. (i) Removing foregoing photoresist. (j) Backside release by DRIE. 56x39mm (300 x 300 DPI)


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Figure 9. XRD pattern of the as-grown AlN piezoelectric thin film. The inset shows the rocking curve of the (002) orientation of the AlN thin film. 57x40mm (300 x 300 DPI)



Graphics for TOC 35x33mm (300 x 300 DPI)


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Electric Field Stiffening Effect in c-Oriented Aluminum Nitride

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