The influence of design parameters on the performance of FBAR in 10–14 GHz

This research presents the analysis of the influence of design parameters on the performance of film bilk acoustic wave resonator (FBAR) working from 10 GHz to 14 GHz. The analysis is done by implementing one-dimensional (1-D) modellings, which are 1-D Mason model and Butterworth Van Dyke (BVD) model. The physical parameters such as piezoelectric materials and its thickness, and size of area affecting the characteristics of the FBAR are analyzed in detail. Zinc oxide (ZnO) and aluminum nitride (AlN) are chosen as the piezoelectric materials. The resonance area is varied at 25μm×25μm to 35μm×35μm. From the analysis, it is found that as the frequency increases, the thickness of the piezoelectric material decreases. Meanwhile, the static capacitance increases as the frequency increases. It is also found that as the area increases, the electrical impedance and static capacitance also increases.


Introduction
High demand for wireless communications technology and video has led to demand for more channels and wider bandwidth.Conventional frequency bands (below 6 GHz) are too congested.Therefore, to meet this demand, the study on the receiving system that works at frequency higher than 10 GHz has increased.Film bulk acoustic wave resonator (FBAR) filters and FBAR diplexers designed using microelectromechanical system (MEMS) technology have been widely used for WiFi and WiMAX applications.Such MEMS components have shown better performance and a higher integration level, and the same performance is expected to be achieved in Ku-band transceivers by using FBAR filters.FBARs operating in the frequency range of 5 GHz to 20 GHz have been reported to show a very high quality (Q) factor, good power handling and small size.The most common piezoelectric materials used for development of FBAR are aluminum nitride (AlN) and zinc oxide (ZnO) [1][2][3][4].FBARs based on lead zirconate titanate (PZT) and cadmium sulphide (CdS) are also found in the literature [5][6].CdS has low acoustic impedance and an electromechanical coupling coefficient (~2.4%).PZT has good performance in terms of the electromechanical coupling coefficient (k 2 eff) values of 19.8%, but has high intrinsic losses at high frequencies [1].Thus, PZT is mostly used for low-frequency FBAR devices or applications that do not require a high Q factor [7].For higher frequency applications, ZnO and AlN are the most suitable piezoelectric materials.These materials have the same hexagonal wurtzite structure.Although the coupling coefficient of ZnO is higher than AlN, AlN is superior to ZnO due to its moderate mechanical coupling factor, higher acoustic velocity and higher Q value.This makes AlN suitable to fabricate bulk acoustic wave (BAW) resonators/filters in several gigahertzes (GHz).Furthermore, AlN is compatible with CMOS technology and more easily manufactured compared to ZnO [7][8].
Modelling is a fundamental step in analyzing the performance of an FBAR.Several 1-D models have been proposed in order to characterize the electrical behavior of the FBAR.The 1-D Mason model is mainly used to represent the electrical behavior of BAW resonators and has been widely employed in work related to it [9][10].The Krimholtz-Leedom-Matthaei (KLM) and Butterworth Van Dyke (BVD) model also provide a very good approach for characterizing the electrical behavior of the FBAR at fundamental modes and higher harmonics [11][12].Therefore, in this work, the both models are implemented in the simulation in order to characterize the performance of the FBAR.

FBAR Concept
FBAR is one of the technologies for fabricating BAW devices, the first FBAR device being released by Lakin and Wang in 1981.Figure 1 shows the acoustic wave propagation in FBAR through its active layer structure, which is usually a piezoelectric material.The acoustic wave causes the deformation of the piezoelectric material.Therefore, the actuation and detection mechanisms involved in FBAR operation are due to the piezoelectric and inverse piezoelectric effects.By using these principles, a voltage applied to the resonators electrodes induces strain of the acoustic layer, and vice versa, and following a mechanical strain of the acoustic layer a voltage can be read out of the electrodes [13].
The resonance frequency of an FBAR operating in fundamental, longitudinal mode is determined mainly by the thickness (t) of the piezoelectric layer given as: where θ is the phase, υ D is acoustic velocity, f is the frequency of acoustic wave propagating through the bulk acoustic layer and t is the thickness of the piezoelectric film.The acoustic velocity can be calculated using the approximation given as : where c D 33 is the elastic stiffness at constant electric displacement and ρ is the density of the piezoelectric material.
At resonance (f=f0), the acoustic phase of the film is θ=π, under these conditions, the f0 can be calculated as in [13]: From Equation 3, it follows that resonance occurs when the film thickness is equal to half the wavelength of the acoustic wave.As shown in Fig. 1, the acoustic wave is confined by the reflecting electrode surfaces at the thin film interface where t must be half the acoustic wavelength, ignoring the electrode loading effects.

1-D Mason Model
The Mason model has been widely used in deriving solutions for the wave propagation through the acoustic layer by using the network theory approach.Fig. 2 shows the thickness excitation of the piezoelectric layer, ignoring the electrodes.The piezoelectric layer can be seen as a three-port component.Two ports are the mechanical ports presented by the forces (F) and the displacement velocity (ν).The other port is the electrical port given by voltage (V) and current (I).
The electrical input impedance of a single piezoelectric layer is given as: where d is the thickness of the piezoelectric layer.F1 and F2 are the forces on the top and bottom surface of the resonator, respectively.v1 and v2 represent the acoustic velocities of the top and bottom surface plane of the resonator, respectively.V is the external electric voltage and I is the current.C is the static capacitance, ω=2πf is the angular frequency,  =   where νL is the longitudinal acoustic wave velocity and h=e/εs where e is piezoelectric coefficient and εs is the permittivity of the piezoelectric layer.kt 2 can be computed using equation 2; while C0 is given in equation 6 where A is the area.

BVD Model
The Mason model may be simplified to the six-lumped element model under the assumption that FBARs have very thin electrodes.The Butterworth-Van Dyke (BVD) model is a common lumped element equivalent circuit model used by the crystal filter to simplify the transcendental functions that totally characterize the resonators used as filter elements.This BVD model, as shown in Fig. 3 (a), comprises of a series motional inductor (Lm), motional capacitor (Cm) and motional resistor (Rm) resonator in parallel with static capacitance (Co).The Co is the electrical capacitance between the two electrodes through which the electric fields are applied.The motional components (Cm, Lm and Rm) represent the electromechanical response of a piezoelectric material.BVD model is the most convenient model to use but if the loss from the electrodes is to be considered then the modified Butterworth Van Dyke Circuit (MBVD) as shown in Fig. 3 (b) is adopted instead.The MBVD includes the dielectric loss (Ro) of the piezoelectric material and electrical losses (Rs) of the electrodes [14].This model provides a better method, both simple and accurate, for characterizing electrical behavior of the FBAR at fundamental modes and higher harmonics and designing bandpass filters [11][12][13][14].Several methods can be found in the literature to calculate the Q factor, for example, calculations based on the BVD) model or evaluation from the phase angle (imaginary part) of the electrical impedance given as: where fs and fp are the resonance frequencies and Zin is the electrical impedance of the FBAR.

Influence of Different Piezoelectric Materials
In this 1-D modelling, the effect of electrodes on fs and fp is ignored.By referring to the estimation given in [7] for the purpose of this analysis, the bottom and top electrodes, Ru is set to 50 nm.Fig. 4 shows the relationship between resonance frequency and piezoelectric thickness.The simulation result indicates that as the thickness of the AlN and ZnO increases, the series resonance frequency decreases.This suggests that a thicker piezoelectric film reduces the influence of the electrode thickness upon the resonance frequency.This occurrence is supported by the notion that the acoustic path is proportional to the piezoelectric film thickness as modelled in equation 4. The piezoelectric film thickness is directly proportional to the acoustic path and inversely proportional to the resonance frequency.As seen from the graph too, the thickness of AlN is thicker than ZnO at the same working frequency.For example, FBAR working at 10 GHz, the thickness of AlN required is 0.553µm.Meanwhile, the thickness of ZnO is 0.318µm.This is due higher acoustic velocity of AlN which is 11050 m/s compared to ZnO that has 6350 m/s.This is true as given in equation 3.
Fig. 5 shows the relationship between different piezoelectric materials and their thicknesses on static capacitance, C0.The results show as the frequency increases, the static capacitance gradually increases too for both AlN and ZnO.This can be verified by using equation ( 6), where the static capacitance is inversely proportional to the thickness of the piezoelectric material.

Influence of Different Area Size
Table 1 and Table 2 summarizes the influence of the resonance area on the electrical impedance, Zin of FBAR using AlN and ZnO respectively.The area is set to 25x25 μm 2 , 30x30 μm 2 and 35x35 μm 2 for each frequency.It is observed that as the resonance area increases, there is no significant change in the resonance frequencies, fs and fp.However the electrical impedance of the FBAR decreases as the resonance area increases.
According to equation 4, this is true as the electrical impedance is inversely proportional to resonance frequency.Fig. 6 and Fig. 7 shows the influence of different area size on the static capacitance of FBAR using AlN and ZnO respectively.From the graphs, it is clear that value of static capacitance is proportional to the size of area for both materials.Therefore, as the area size increases, the static capacitance increases too.This is verified by using equation 6.As seen from the graphs too, it is found that the values of static capacitance is higher for FBAR using ZnO compared to FBAR using AlN at the same working frequency.This is due to the permittivity value of ZnO is slightly lower than AlN.The permittivity of AlN and ZnO is 9.5 and 9.2 respectively.
From the analysis in section 3.1 and 3.2, the finding shows that the resonance frequency of FBARs is determined by the thickness and phase velocity of the piezoelectric layer.Therefore, for FBARs operating at frequencies higher than 10 GHz, the thickness of the piezoelectric layer is in the hundred nanometre (nm) scale.Furthermore, the properties and thickness of the piezoelectric materials have a significant influence on the performance of the FBAR in terms of resonance frequency, static capacitance and the electrical impedance of the FBAR.

Conclusion
This work presented the design and analysis of FBAR using 1-D modelling.The influence of various geometrical parameters on FBAR performance were analysed and explored to find suitable solutions for designing FBAR operates at frequency higher than 10 GHz with a high Q factor and wide bandwidth.However, the presence of spurious modes at the frequency of interest due to lateral waves cannot be predicted by 1-D modelling, therefore, the threedimensional (3-D) simulation tool will be beneficial in future work.

Fig. 4 .
Fig. 4. Influence of Different Piezoelectric Materials and Thickness on Frequency

Table 1 .
Influence of Area Size on Impedance, Zin using AlN.

Table 2 .
Influence of Area Size on Impedance, Zin using ZnO.