Design of proposed patterned-ZnO/Si SAW devices using equivalent

devices on silicon with oxide buffer layer is shown in Fig. 3.22. The equivalent circuit has been modeled based on the equivalent circuit models of SAW devices reported by Nordin [29], Thompson [5], and Venema [62]. The equivalent circuit model of a conventional SAW device has been discussed in Chapter 2. The acoustic wave propagation is modeled by a series RLC circuit in parallel with a parasitic capacitor (C0), and Rx, Lx, Cx, define the radiation resistance, motional inductance and motional capacitance respectively. C^ox exists due to the presence of oxide layer in the structure and is formed between source electrode and ground electrode. The oxide capacitance Cox is given by

𝐶𝐶𝑜𝑜𝑜𝑜 =𝑊𝑊ε𝑜𝑜𝑜𝑜𝑁𝑁𝑃𝑃 (3.4)

where W is the aperture length of the IDT, εox is the permittivity of oxide layer and NP is the number of finger pairs in the IDT.

The total transducer capacitance (C^T) for the proposed structure with an oxide film is given by

𝐶𝐶𝑇𝑇 =𝑊𝑊ε𝑍𝑍𝑍𝑍𝑍𝑍(2N𝑃𝑃−1) +𝐶𝐶𝑜𝑜𝑜𝑜 (3.5)

where εZnO is the permittivity of ZnO and is equal to 135 pF/m [26], and 𝑊𝑊ε_{𝑍𝑍𝑍𝑍𝑍𝑍}(2N_𝑃𝑃−1) is equivalent to transducer capacitance without oxide layer.

Fig. 3.21. y-displacement profile of patterned-ZnO/IDT/2µm-SiO2/Si SAW delay line at 34.16 ns.

Addition of SiO² buffer layer has reduced the acoustic radiation into bulk and increased acoustic energy concentration near the surface as compared to the results shown in Fig. 3.18 (a) for patterned-ZnO/IDT/Si SAW delay line.

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Chapter 3 Design and Simulation of Patterned-ZnO/Si SAW Devices

A sinusoidal input Vin is applied to IDT results in excitation of bulk waves inside the ZnO pattern and the bulk waves are mode converted into surface waves that propagate along the silicon substrate. When the acoustic waves are incident at the output IDT with patterned-ZnO structure, the surface waves are converted back to bulk waves in ZnO and a portion is radiated into the bulk of silicon. The BAW excited in ZnO pattern will induce an alternating current Iout in the load connected to the output IDT. The ratio of Iout/Vin is known as forward admittance and real part of admittance (Ga) is known as radiation conductance [29] and is approximated as

𝐺𝐺_𝑎𝑎=8𝑓𝑓_𝑟𝑟𝐾𝐾²𝐶𝐶_𝑇𝑇𝑁𝑁_𝑃𝑃 (3.6) where K² is the electromechanical coupling coefficient and fr is the resonance frequency of the device obtained from the FE simulations.

The conductance of device is given by

𝐺𝐺_𝑠𝑠(𝑓𝑓_𝑟𝑟) =𝐺𝐺_𝑎𝑎�1 + 2Γ𝐶𝐶𝐶𝐶𝐶𝐶(4𝜋𝜋𝜋𝜋) +Γ²

1−Γ² � (3.7)

where Γ is reflection coefficient of the reflector grating structure and 𝜋𝜋 is given by 𝜋𝜋=𝐿𝐿_𝑔𝑔+ 𝐿𝐿_𝑝𝑝+^{𝑁𝑁𝑃𝑃}₂^𝜆𝜆 [29] where Lg is the distance between IDT and grating structure, Lp is the

SiO2

Silicon substrate

Vin Gnd

CT CT CT

Cox Cox

Cx

Rx

Lx

C0

Rs

Rs

Vin

Iout

Acoustic equivalent circuit

Vin Gnd

Fig. 3.22. Equivalent circuit model of the proposed ZnO-patterned structure on silicon with oxide layer.

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Chapter 3 Design and Simulation of Patterned-ZnO/Si SAW Devices penetration depth of acoustic wave along the grating, and Np is the number of finger pairs in IDT structure. The acoustic equivalent circuit parametersare obtained as follows [29]

Acoustic resistance Rx = 1/𝐺𝐺_𝑠𝑠(𝑓𝑓_𝑟𝑟) (3.8) Inductance Lx = ^{𝐿𝐿+2𝐿𝐿}_𝐺𝐺 ^𝑝𝑝

𝑎𝑎𝜐𝜐 ∙_1+2Γ𝐶𝐶𝑜𝑜𝑠𝑠(4𝜋𝜋𝜋𝜋)+^Γ2 Γ² (3.9)

Acoustic capacitance Cx = _4𝜋𝜋2¹_𝑓𝑓

𝑟𝑟2𝐿𝐿_𝑥𝑥 (3.10)

Feed through capacitance Cf = ^{𝐵𝐵𝑊𝑊}_𝐿𝐿

𝑐𝑐 (3.11)

Using the equations (3.5 and 3.6), the number of finger pairs and the aperture length of IDT are chosen in such a way that the impedance of IDT at the operating frequency matches with the source impedance and load impedance, normally 50 Ω. The following section describes the design of SAW devices with patterned-ZnO structure on silicon.

3.5.1 Calculation of IDT parameters for proposed SAW devices on silicon

The IDT parameters for one port SAW resonators, two port SAW resonators, and SAW delay lines are calculated using above mentioned equivalent circuit model and used for device fabrication. The above mentioned equations are written in MATLAB to obtain the IDT dimensions with desired 50 Ω impedance.

From Table 3.1, it is noticed that h/λ = 0.19 exhibits high K² and high phase velocity for patterned-ZnO/Si structure. Hence, for the fabrication of proposed devices, the ZnO film thickness of 3.04 µm chosen for an IDT wavelength of 16 µm. In the phase velocity and K² characteristics, at h/λ = 0.19, VPT1 mode exhibits K² value of 6.4% and phase velocity of 5072 m/s which corresponds to the device operating frequency of 317 MHz. Substituting the values of K² and operating frequency in equation (3.6), aperture (W) and number of finger pairs (NP) are calculated. In general, to reduce the diffraction effects of the generated surface waves, it is advisable to have aperture length greater than 50λ [5]. Accordingly the aperture length is decided and the respective number of finger pairs is calculated. The penetration depth of the generated surface modes is estimated by calculating reflection coefficient k, which is reflectivity of surface wave for one electrode finger in the grating structure and is given by [29]

𝑘𝑘=𝑗𝑗|0.5 𝐾𝐾²|𝜋𝜋

2�(−cos∆) +� 𝑃𝑃_0.5(cos∆)

𝑃𝑃_−0.5(−cos∆)�� (3.12) where ∆=𝑛𝑛𝜋𝜋 and n is metallization ratio.

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Chapter 3 Design and Simulation of Patterned-ZnO/Si SAW Devices In this design n of 0.5 is considered, Legendre polynomials 𝑃𝑃0.5(cos∆) =1.5061 and 𝑃𝑃−0.5(−cos∆) = 1.328 are adapted from Nordin [29].

The total reflectivity of the grating structure is given by (3.10) and ideally should be ~1.

Γ= tanh (𝑁𝑁𝑘𝑘) (3.13)

Using the reflection coefficient, the penetration depth Lp is calculated using the following formula

𝐿𝐿_𝑝𝑝=𝜆𝜆/(4|𝑘𝑘|) (3.14)

Using the above mentioned equations, with K² value of 6.4% and operating frequency 317 MHz the calculated IDT parameters are as follows

From (3.12) reflection coefficient of an electrode in the grating structure k = 0.057

Minimum number of electrodes in reflector grating (N) required to ensure complete reflection of SAW at the grating structure is calculated using (3.13), and Γ= 0.99 is assumed and the number of electrodes in grating structure N = 48.

From (3.14) calculated penetration depth Lp= 70.17 µm.

Table 3.3 Calculated IDT dimensions using equivalent circuit model.

Sr. No. Aperture length (W) Number of finger pairs (N)

1 55 λ 65

2 60 λ 63

3 65 λ 60

4 75 λ 58