Effects of Electric Bias on Different Sc-Doped AlN-Based Film Bulk Acoustic Resonators

Abstract

Film bulk acoustic resonators (FBARs) based on aluminum nitride (AlN) and scandium-doped aluminum nitride (AlScN) exhibit tremendous application aspects in the radio frequency front-end due to achievable high-frequency characteristics, superior thermal performances and compatibility with harsh environments. Delicately controlling the resonant frequency (f_s) of FBAR is essential for integrating filters or modules. In this work, we provide a practical feasibility in adjusting f_s of AlN and AlScN FBAR using external direct current electric bias (E_DC). When applying a negative E_DC (the direction along the reversed c-axis), f_s shifts to a lower frequency, whereas a positive E_DC brings a higher f_s. In order to extract the equivalent values of the stiffness coefficient (c₃₃), piezoelectric coefficient (e₃₃) and dielectric constant (ε_zz) of AlN and AlScN piezoelectric materials, we adopted the electromechanical equivalent Mason model. The results show that the equivalent values of c₃₃ increase with the change of E_DC from negative to positive, and, on the other hand, those of e₃₃ and ε_zz decrease. Our work provides a systematic investigation on the electric field-influenced stiffening effect of AlN and AlScN piezoelectric films and opens a feasibility for frequency-tunable resonators.

1. Introduction

AlN piezoelectric thin film exhibits the advantages of high acoustic velocity, high thermal conductivity and complementary metal-oxide-semiconductor (CMOS) integration compatibility [1,2], and therefore becomes the potential choice for film bulk acoustic resonators (FBARs) [3,4,5] and radio frequency (RF) filters [6]. With doping Sc, the piezoelectric strain coefficient d₃₃ of AlScN thin film can be four times higher than pure AlN film [7], thus AlScN piezoelectric thin film shows a greater advantage for emerging FBARs [8,9,10].

The center frequency and band gap of the RF filters are decided by the resonant frequency (f_s) and anti-resonant frequency (f_p) of FBARs [11]. FBARs with precisely controlled and adjustable frequency are desired for designing RF filters. Many efforts have been devoted to achieving frequency tunable FBARs, such as adding external micro-heater elements [12] or capacitors [13] into the circuit. Resonant characteristics of FBARs are mainly determined by the piezoelectric thin films, as the stiffening effect of piezoelectric film can be influenced by electric field [14,15,16,17,18,19], in this aspect, we can use direct current (DC) electric field to modulate f_s of FBARs. Although several works have been performed to study the influence of external electric field on AlN-based FBARs [16,17], with the extension for Sc-doped AlN on FBARs, the relationship between stiffening effect and electric field for AlN and AlScN, the corresponding responses of AlN and AlScN-based FBARs for different electric fields still need further investigation.

In this work, we study the resonant characteristics of FBARs with different external DC electric fields (E_DC) and explore the stiffening effect of AlN, Al_0.8Sc_0.2N and Al_0.7Sc_0.3N thin films. With a negative E_DC (the direction along reversed c-axis for AlN and AlScN films), f_s shifts to a lower value due to the stiffening effect of AlN and AlScN films.

Using Mason equivalent electric model, we extracted the equivalent value of stiffness coefficient c₃₃, piezoelectric coefficient e₃₃ and relative dielectric constant ε_r of AlN, Al_0.8Sc_0.2N and Al_0.7Sc_0.3N thin films. When E_DC changes from −100 MV/m to 100 MV/m, the value of equivalent c₃₃ increases, in contrast, the values of equivalent e₃₃ and ε_r decrease. The results are compatible with the math model we deduced from the Gibbs electric energy expansion equation. In our work, we provide the experimental data of the effect of electric bias on FBAR along with the theoretical basis, realizing frequency tunable AlN and AlScN-based FBAR devices which show potential prospects in RF applications.

2. Device Design, Fabrication and Characterization

In this work, FBARs adopted AlN, Al_0.8Sc_0.2N and Al_0.7Sc_0.3N piezoelectric thin films, respectively. The piezoelectric films were deposited under 200 °C by a magnet sputter (Sigma fxP system) using physical vapor deposition (PVD) technology with sputter power of 6 kW and bias power of 161 W. The targets for AlN and AlScN are Al metal and Al-Sc alloy (the mass ratio of Sc and Al is 20%) and were ~6 cm from the 8-inch high-resistivity Si substrate, which is in the orientation of <111>. The flow rates of Ar and N₂ gas are 20 sccm and 60 sccm, respectively.

The scanning electron microscope (SEM) result of the surface morphology of AlN-based FBAR is shown in Figure 1a. The designed devices contain top electrical signal pad (S_T) and bottom electrical signal (S_B), which are connected to the top and bottom pentagonal Mo electrodes of FBAR, respectively. The cross-sectional view of AlN-based FBAR shows that the AlN piezoelectric layer is sandwiched with top and bottom Mo electrodes, as is depicted in Figure 1b. In order to promote the orientation quality of c-axis oriented piezoelectric material, an AlN seed layer was used for the deposition of the piezoelectric thin film [20,21]. After slicing the 8-inch device wafer into 1 cm² piece by a diamond pen, the structures of piezoelectric films were characterized by X-ray diffraction (XRD) measurement, as shown in Figure 1c. The results show that AlN thin film, Al_0.8Sc_0.2N thin film and Al_0.7Sc_0.3N thin film have a diffraction peak when 2θ equals 36.05°, 36° and 36.2°, respectively, suggesting that AlN and AlScN thin films grow in the c-axis orientation and have a wurtzite structure [19]. The frequency-impedance curves of FBARs characterizing the frequency response of FBARs were measured with a Keysight N5222B network analyzer. As shown in Figure 1d, the DC electric bias potential (V_DC) created by voltage source was combined with RF signal (V_RF) by a Bias Tee. To investigate the influence of external bias on the resonant characteristics of FBARs, the combination of potential (V_RF + V_DC) was applied to the FBAR.

Figure 2 shows the brief fabrication process of the proposed FBARs. The fabrication process includes four masks and can be detailed as: (a) A 2.5 µm thick cavity was created by deep reactive ion etching (DRIE) using the first mask; (b) SiO₂ was deposited. After dry etch, SiO₂ was polished by chemical mechanical polishing (CMP) to be flush with the surface of Si substrate; (c) a 25 nm thick AlN seed layer was grown; (d) the Mo bottom electrode layer was patterned as a pentagon on the AlN seed layer after Mo deposition; (e) Piezoelectric thin film was sputter deposited on the bottom electrode; (f) the Mo top electrode was sputter-deposited and patterned as a pentagon on the piezoelectric thin film; (g) the cavity filled with SiO₂ was released by buffered oxide etch (BOE). The details of these FBARs are listed in

Table 1. The thickness of each layer, the concentration of Sc, the density of piezoelectric thin film and the area of resonators.

Sc (%)	Top Electrode (nm)	Piezoelectric Material (nm)	Bottom Electrode (nm)	AlN (AlScN) Density (kg/m3) [22]	Area (μm2)
/	290	835	308	3260	12,860
20	168	575	167	3317	3561
30	108	516	98	3373	1046

.

3. Results and Discussions

We used different E_DC to investigate the resonant characteristics of FBARs and stiffening effects of AlN, Al_0.8Sc_0.2N and Al_0.7Sc_0.3N piezoelectric films. As is shown in Figure 3a, obvious frequency shifts for FBARs were observed under different E_DC. Figure 3b shows the comparison curves of f_s and f_p of FBARs with piezoelectric materials, AlN, Al_0.8Sc_0.2N and Al_0.7Sc_0.3N under varying E_DC. f_s and f_p of all FBARs increase with the increment of E_DC from −100 MV/m to 100 MV/m (positive E_DC pointing to the bottom electrode).

To determine the relationship between piezoelectric parameters (c₃₃, e₃₃ and ε_zz) of piezoelectric materials and E_DC, the full diffraction of Gibbs electric energy equation was introduced [23] as:

$$d{G}_2=-\sigma d\theta +TdS-DdE$$

(1)

where G₂ is the Gibbs electric energy, $\sigma$ is entropy, $\theta$ is temperature and T and S represent stress and strain, respectively. D and E are the electric displacement and the applied electric field of the piezoelectric slab, respectively.

We assume that S and E are non-zero terms along the thickness direction [15], the third-order expansion formula of Gibbs electric energy can be written as:

$$G_2-G_{2,0}=\frac{1}{2}{c}_{33}{S}^2-\frac{1}{2}{\epsilon }_{zz}{E}^2-e_{33}ES+G{E}^{2}S+NE{S}^2+\frac{1}{3}O{E}^3+\frac{1}{3}R{S}^3$$

(2)

where G and N represent electro strictive coefficients. O and R are non-linear variations of the dielectric constant and the stiffness, respectively. The partial derivatives of G₂ with respect to S and E are:

$${\left.\frac{\partial G_2}{\partial S}\right|}_E=T=c_{33}S-e_{33}E+2NES+G{E}^2+R{S}^2$$

(3)

$${\left.\frac{\partial G_2}{\partial E}\right|}_S=-D=-{\epsilon }_{zz}E-e_{33}S+2GES+N{S}^2+O{E}^2$$

(4)

When a combination of RF signal and DC potential (V_RF + V_DC) electric excitation is applied to FBARs, Equations (3) and (4) can be written as:

$$\tilde{T}=\left(c_{33}+2N{E}_{DC}+2R{S}_{DC}\right)S-\left(e_{33}-2N{S}_{DC}-2G{E}_{DC}\right)E$$

(5)

$$\tilde{D}=\left(e_{33}-2N{S}_{DC}-2G{E}_{DC}\right)S+\left({\epsilon }_{zz}-2G{S}_{DC}-2O{E}_{DC}\right)E\#$$

(6)

where $\tilde{T}=T+T_{DC}$, $\tilde{D}=D+D_{DC}$.

T_DC and D_DC refer to the stress and electric displacement caused by E_DC. When only considering the effect of E_DC, $\tilde{T}$ equals 0. When only keeping the first-order terms, the strain under E_DC (S_DC) can be calculated by Equation (5):

$$S_{DC}=\frac{e_{33}{E}_{DC}}{c^E}$$

(7)

By substituting Equation (7) into Equations (5) and (6), we finally obtain:

$$c_{eql}=c_{33}+2E_{DC}\left(N+\frac{e_{33}R}{c_{33}}\right)$$

(8)

$$e_{eql}=e_{33}-2E_{DC}\left(G+\frac{e_{33}N}{c_{33}}\right)$$

(9)

$${\epsilon }_{eql}={\epsilon }_{zz}-2E_{DC}\left(O+\frac{e_{33}G}{c_{33}}\right)$$

(10)

where c_eql, e_eql and ε_eql represent the equivalent values of c₃₃, e₃₃ and ε₃₃ of the FBAR devices under E_DC. Equations (8)–(10) indicate that, when ignoring the higher order terms of Gibbs electric energy equation, the equivalent stiffness will increase linearly with E_DC, whereas the piezoelectric coefficient and dielectric constant will decrease linearly with E_DC.

The pre-strain caused by E_DC results in the shifts of f_s and f_p of AlN or AlScN-based FBARs. Moreover, the pre-strain also results in the change of equivalent stiffness. We adopted an electromechanical equivalent Mason model of FBARs to investigate the quantitative relationship between equivalent stiffness and E_DC. [24,25], which is depicted in Figure 4.

According to the transmission line theory, the admittance expression [19] of the resonator can be derived as:

$$Y=\frac{M_{22}}{M_{12}}$$

(11)

M₁₂ and M₂₂ are elements of matrix M. M is a second-order matrix given by:

$$\mathit{M}=\left[\begin{array}{cc}1& 0\\ i\omega C_0& 1\end{array}\right]\left[\begin{array}{cc}1& i\omega C_0\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1/n& 0\\ 0& n\end{array}\right]{\mathit{M}}_{\mathbf{1}\mathbf{,}\mathbf{2}}{\mathit{M}}_{\mathbf{3}}{\mathit{M}}_{\mathbf{4}}$$

(12)

where C₀ is the static capacitance of the resonator. n is the electromechanical conversion factor. In addition, M_1,2 is the equivalent transmission matrix for the Mo top electrode and the piezoelectric layer; and M₃ and M₄ are the transmission matrixes for the Mo bottom electrode and AlN seed layer, given by:

$${\mathit{M}}_{\mathbf{1}\mathbf{,}\mathbf{2}}=\left[\begin{array}{cc}\frac{b_2}{a_1+a_2+\frac{a_1{b}_1}{a_1+b_1}}+1& \frac{b_2{a}_2}{a_1+a_2+\frac{a_1{b}_1}{a_1+b_1}}+a_2\\ \frac{b_2}{a_1+a_2+\frac{a_1{b}_1}{a_1+b_1}}& \frac{a_2}{a_1+a_2+\frac{a_1{b}_1}{a_1+b_1}}+1\end{array}\right]$$

(13)

$${\mathit{M}}_{\mathit{k}}=\left[\begin{array}{cc}\frac{a_k}{b_k}+1& 2a_k+\frac{a_k^2}{b_k}\\ \frac{1}{b_k}& \frac{a_k}{b_k}+1\end{array}\right], k=1,3,4$$

(14)

$$\left\{\begin{array}{c}{a}_m=i{\rho }_m{v}_{m}Atan\left(\frac{k_m{d}_m}{2}\right)\\ b_m=\frac{{\rho }_m{v}_{m}A}{isin\left(k_m{d}_m\right)}\\ v_m=\sqrt{c_m/{\rho }_m}\\ k_m=\frac{\omega }{v_m}=2\pi f/v_m\end{array}\right., m=1,2,3,4$$

(15)

where the subscripts “1”, “2”, “3” and “4” denote the top electrode material, piezoelectric material, bottom electrode material and seed layer, respectively. ρ_m, c_m and d_m represent the density, Young’s modulus and the thickness of the corresponding material. A represents the effective resonance region of the FBAR. c₂ represents the Young’s modulus of piezoelectric layer of FBAR and can be described by:

$$c_2=c_{33}+\frac{e_{33}^2}{{\epsilon }_0{\epsilon }_r}$$

(16)

The equivalent piezoelectric parameters, such as c₃₃, e₃₃ and ε_r, can be extracted by fitting-simulated impedance-frequency curves of the Mason model with the measured impedance-frequency curves of FBARs. The extracted values of equivalent piezoelectric parameters with different E_DC are shown in Figure 5. The results show that with the increment of E_DC, the value of c₃₃ will increase approximately linearly with E_DC, whereas e₃₃ and ε_r will decrease approximately linearly with E_DC. The experimental results agree with the deduction of Equations (8)–(10). With the increment of the doped concentration of Sc in AlScN piezoelectric film, the value of c₃₃ of AlScN thin film decreases, while the values of e₃₃ and ε_r of AlScN thin film increase under the same electric excitation. The insertion of Sc element changes the lattice constant of AlN material, increasing the internal axial strain sensitivity of AlScN thin film [26] and is responsible for the increment of e₃₃ and piezoelectric modulus (d₃₃) and results in the decrement of c₃₃ [27].

When the RF exciting signal is applied to the FBAR by connecting the signal to the top and bottom electrodes, an alternating electric field is created along the c-axis of the FBAR [11]. The piezoelectric film vibrates along the c-axis due to the piezoelectric effect and creates strain and stress along the c-axis as well, when the frequency of RF signal equals to the f_s of the FBAR [19]. According to the transmission line theory of the acoustic wave in FBAR, the f_s of the FBAR is decided by not only the geometry of each layer but also the characteristic parameters, such as the density, Young’s modulus, etc. The polar atoms in the AlN and AlScN lattice drift away from the original balanced position if an extra E_DC is applied to the AlN and AlScN piezoelectric films. When the external field is positive (the direction of E_DC is along with the direction from the top electrode to the bottom electrode), considering the piezoelectric effect, the aluminum and scandium atoms will move towards nitride atoms. However, when E_DC is negative, the aluminum and scandium atoms move away from nitride atoms [19]. The existence of pre-strain created by the external field changes the resonant parameters of FBARs. The movement of atoms in the piezoelectric film changes the equivalent stiffness of the material, resulting in the shifts of f_s and f_p.

In this work, compared with the research on the effect of E_DC on single material, for example, AlN [19] or Al_0.7Sc_0.3N [10], we adopted three different Sc-doped concentrations of AlN piezoelectric material and gave the comparison of experimental results of the effects of E_DC for these three materials. Moreover, by providing the theory basis of the change of resonant parameters under E_DC, we move forward in the study of electric biasmodulated FBARs.

4. Conclusions

In this work, we applied the combined V_RF and V_DC potentials to FBARs with AlN, Al_0.8Sc_0.2N and Al_0.7Sc_0.3N thin films to investigate the effect of an external electric field on resonant characteristics of FBARs. To further understand the theoretical basis, we deduced the relationship between piezoelectric parameters (c₃₃, e₃₃ and ε_zz) and E_DC using the Gibbs electric energy equation and equivalent Mason model. The results show that with the change of E_DC from −100 MV/m to 100 MV/m, the f_s and f_p of all FBARs with AlN, Al_0.8Sc_0.2N and Al_0.7Sc_0.3N thin films increase due to the stiffening effects of AlN and AlScN films. Although the Sc doping changes the piezoelectric characteristics of AlN films by increasing e₃₃, ε_zz and reducing c₃₃, the varying trends of stiffening effects with E_DC are similar for AlN, Al_0.8Sc_0.2N and Al_0.7Sc_0.3N thin films. The electric field tunable FBARs based on AlN and AlScN piezoelectric films demonstrate a promising way for the frequency tuning of resonators and filters in telecommunication applications.