Introduction

Lithium niobate (LN, or LiNbO3) is a multifunctional crystal characterized by its nonlinear optical, electro-optic, piezoelectric, ferroelectric, and thermoelectric properties. Referred to as “the silicon of photonics”, the LN is a promising material for photonics1,2,3,4,5 and electro-optics6,7,8,9. Additionally, owing to the prominent piezoelectric effect, the LN is extensively applied to acoustic resonators10,11,12,13, acoustic filters14,15,16,17, piezoelectric micromachined ultrasonic transducers (PMUT)18, and sensors19. From the 2G to 5G sub-6 GHz wireless communication terminals, the piezoelectric acoustic filter chips with small size and high selectivity are dominant. However, the millimeter-wave piezoelectric acoustic filter chips suffer from narrow bandwidth and large insertion loss (IL) due to the limited electromechanical coupling coefficient and low quality factor at millimeter wave. Therefore, electromagnetic millimeter-wave filter chips are the main solutions for millimeter-wave systems. Existing approaches primarily rely on low-K materials to mitigate loss, but this strategy inherently limits the device size reduction. Therefore, this work proposes to utilize LN for millimeter-wave filters, considering the high-K feature of LN with the properties of low dielectric loss, ease of fabrication, and low cost. Figure 1a illustrates the multi-physical platform of LN for photonics, acoustics, and electromagnetics, while Fig. 1b presents the applications in LN-based millimeter-wave filter chips.

Fig. 1: Illustration of multi-physical platform of LN and its applications in millimeter-wave filter chips.
Fig. 1: Illustration of multi-physical platform of LN and its applications in millimeter-wave filter chips.
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a Multi-physical platform of LN. b LN-based millimeter-wave filter chips

The Shannon theorem highlights the potential of the millimeter-wave spectrum, which offers substantial bandwidth that can increase communication capacity20,21,22. To support high data rate, low latency, large capacity, and large deployment density in 5G/6G systems, millimeter-wave filters must be not only highly selective but also compact and efficient. However, the low-cost millimeter-wave filter chips with small size and high selectivity are extremely challenging. As larger permittivity leads to larger dielectric loss and conductor loss, current filter designs are primarily based on low-K materials and face challenges in achieving miniaturization. The high-K, near-defect-free material is essential to push the boundaries of filter miniaturization while maintaining low losses.

In the past, plenty of millimeter-wave filters have been presented by using the printed circuit board (PCB) process23,24,25,26,27,28,29,30,31. A microstrip millimeter-wave bandpass filter (BPF) using the PCB process was presented with the center frequency (f0) of 32 GHz, the measured IL at f0 of 3.5 dB, and the measured return loss (RL) at f0 of 10 dB23. A substrate integrated waveguide (SIW) millimeter-wave BPF using the PCB process was presented with the f0 of 25.88 GHz, the minimum IL of 4.36 dB, and the size of 0.84 × 0.53 λ024. A substrate integrated suspended line (SISL) millimeter-wave BPF using the multi-layer PCB process was presented with the f0 of 29.2 GHz, the measured IL at f0 of 1.6 dB, and the fractional bandwidth (FBW) of 10.3%31. For the presented millimeter-wave BPF using the PCB process, the fabrication is convenient and cheap, but the filter size and IL are large.

Taking advantage of the multi-layer structure, the low-temperature co-fired ceramic (LTCC) technology has been widely applied to design millimeter-wave BPFs32,33,34,35,36,37,38,39,40. A SIW millimeter-wave BPF using the LTCC technology was presented with the f0 of 27.95 GHz, the measured minimum IL of 2.8 dB, and the size of 0.57 × 0.3 λ035. A microstrip millimeter-wave BPF using the LTCC technology was presented with the f0 of 60 GHz, the measured minimum IL of 2.8 dB, FBW of 6.6%, and the size of 0.48 × 0.206 λ040. For the presented millimeter-wave BPFs using the LTCC technology, the filter size is relatively small, but the IL is large.

Owing to the size reduction and high-precision fabrication, the integrated passive device (IPD) technology is another widely used method to design millimeter-wave BPFs41,42,43,44,45,46,47,48,49,50. A millimeter-wave BPF using the 0.1-μm gallium arsenide (GaAs) technology was presented with the f0 of 23.5 GHz, the measured minimum IL of 2.9 dB, FBW of 22.2%, and the size of 0.05 × 0.022 λ041. A millimeter-wave BPF using the 130-nm CMOS technology was presented with the f0 of 34.5 GHz, the measured minimum IL of 1.6 dB, FBW of 61.2%, and the size of 0.03 × 0.014 λ045. A millimeter-wave BPF using the 130-nm BiCMOS technology was presented with the f0 of 75.5 GHz, the measured minimum IL of 2.7 dB, FBW of 38.4%, and the size of 0.103 × 0.044 λ050. Despite the advantage of reduced size, IPD-based millimeter-wave filters typically exhibit high IL. Moreover, the IPD-based millimeter-wave filters are much more expensive than the filters based on PCB and LTCC technologies, which turns out to be a obstacle to mass production.

This article proposes and demonstrates the LN-based millimeter-wave BPF chips with ultra-small size and high selectivity by using the microelectromechanical systems (MEMS) microfabrication technology. Firstly, the coplanar waveguide (CPW) half-wavelength resonators and T-shaped slot resonators are applied to construct a second-order LN-based millimeter-wave BPF chip for narrowband millimeter-wave applications. The T-shaped slot resonators are integrated with the CPW half-wavelength resonators, which can suppress not only the first parasitic passband but also reduce the physical size. Then, the CPW half-wavelength resonators, T-shaped slot resonators, and a CPW dual-mode resonator are applied to construct a fourth-order LN-based millimeter-wave BPF chip for wideband millimeter-wave applications. As a high-K material, the LN-based millimeter-wave BPF chips can realize small sizes but bring the issue of high-order modes, which will deteriorate frequency selectivity. To eliminate the influence of high-order modes, the LN thickness is optimized, and then the cutoff frequencies of the high-order modes are elevated to be far away from the desired passband. The proposed LN-based BPFs exhibit ultra-small size, low passband IL, high selectivity, and cost-effective production, making them promising candidates for applications in millimeter-wave wireless communications, sensing, imaging, and quantum information systems.

Results and discussion

Second-order LN-based millimeter-wave BPF chip

The 128° Y-cut LN with a thickness of 0.15 mm is used herein, and the relative permittivity values are: ε11 = 45, ε22 = 38.9, ε33 = 35. Figure 2a presents the top and perspective views of a second-order LN-based millimeter-wave filter chip using the miniaturized CPW half-wavelength resonators. The f0 of the passband can be tuned by the resonator length L3, while the bandwidth of the passband can be adjusted by the coupling coefficient (K) and the external quality factor (Qe), which are calculated by

$$K=\frac{{f}_{u}^{2}-{f}_{l}^{2}}{{f}_{u}^{2}+{f}_{l}^{2}}$$
(1)
$${Q}_{e}=\frac{{f}_{0}}{B{W}_{3dB}}$$
(2)

where fu and fl represent the upper and lower resonant frequencies, respectively. The coupling scheme of the second-order LN-based millimeter-wave BPF chip using the CPW half-wavelength resonators is shown in Supplementary Fig. 1a. Based on the coupling principle, the K can be increased by reducing the coupling gap g1 between two resonators, while the Qe can be increased by increasing the gap g2 between the feeding line and the resonator. As a result, the f0 and bandwidth of the second-order LN-based millimeter-wave filter chip using the CPW half-wavelength resonators can be independently adjusted. However, the parasitic passband occurs at around twice the frequency of the desired passband, which leads to a narrow upper stopband and a low suppression level of the upper stopband. To suppress the first parasitic passband, T-shaped slot resonators are integrated with the CPW half-wavelength resonators. Figure 2b presents the top view and perspective view of the proposed second-order LN-based millimeter-wave BPF chip by using the CPW half-wavelength resonators and T-shaped slot resonators. Each T-shaped slot resonator is equivalent to a capacitor and an inductor connected in parallel, which can create a stopband to suppress the first parasitic passband, resulting in a wide upper stopband and a high suppression level of the upper stopband. The coupling scheme of the second-order LN-based millimeter-wave BPF chip using the CPW half-wavelength resonators and T-shaped slot resonators is shown in Supplementary Fig. 1b. The f0 of the second-order LN-based millimeter-wave BPF chip using the CPW half-wavelength resonators and T-shaped slot resonators can be adjusted by the length L3 as shown in Supplementary Fig. 1c, while the bandwidth can be independently adjusted by the gap g1 as shown in Supplementary Fig. 1d.

Fig. 2: Structure and simulation of second-order LN-based millimeter-wave BPF chips.
Fig. 2: Structure and simulation of second-order LN-based millimeter-wave BPF chips.
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a Top view and perspective view of a second-order LN-based millimeter-wave BPF chip using CPW half-wavelength resonators. The optimized dimensions are: L1 = 3.25, L2 = 0.65, L3 = 1.245, W1 = 2.35, W2 = 0.35, W3 = 0.15, g1 = 0.06, g2 = 0.07, t = 0.015, and h = 0.15, all in mm. b Top view and perspective view of second-order LN-based millimeter-wave BPF chip using CPW half-wavelength resonators and T-shaped slot resonators. The optimized dimensions are: L1 = 2.72, L2 = 0.65, L3 = 0.98, L4 = 0.348, W1 = 2.35, W2 = 0.35, W3 = 0.15, W4 = 0.05, g1 = 0.06, g2 = 0.07, t = 0.015, and h = 0.15, all in mm. c S parameters of second-order LN-based millimeter-wave BPF chips with and without using T-shaped slot resonators. d Frequency responses of second-order LN-based millimeter-wave BPF chip adjusted by length L4 of T-shaped slot resonators

Figure 2c presents the simulated S parameters of the proposed second-order LN-based millimeter-wave BPF chips with and without T-shaped slot resonators. It can be observed that the wide upper stopband and high suppression level are realized by using the T-shaped slot resonators. Figure 2d presents the frequency responses of the second-order LN-based millimeter-wave BPF chip adjusted by the length L4 of the T-shaped slot resonators. The designed value of the length L4 is 0.348 mm for the suppression of the first parasitic passband. Moreover, at the f0 of 26.5 GHz, the length of the CPW half-wavelength resonator is 1.245 mm, while the length of the CPW half-wavelength resonator integrated with a T-shaped slot resonator is 0.98 mm. Thus, the T-shaped slot resonator can not only suppress the first parasitic passband but also reduce the physical size.

Figure 3a presents a photograph of the second-order LN-based millimeter-wave BPF chip using the CPW half-wavelength resonators and T-shaped slot resonators. Two 50-Ohm ground-signal-ground (GSG) probes with a pitch of 0.6 mm are connected to the CPW feeding line for measurements. The size comparison photograph of the fabricated second-order LN-based millimeter-wave BPF chip with a coin is shown in Supplementary Fig. 2a. Figure 3b presents the simulated and measured S parameters of the fabricated second-order LN-based millimeter-wave BPF chip. The simulated f0 is 26.5 GHz, and the 3-dB bandwidth is 23–30 GHz (26.4%). The simulated IL and RL at f0 are 0.97 and 18.04 dB, respectively. From 0 to 12.14 GHz and from 36.57 to 50 GHz, the simulated stopband suppression level (SSL) is over 20 dB. The measured f0 is 25.85 GHz, and the 3-dB bandwidth is 22.2–29.5 GHz (28.2%), which can cover the n257 and n258 5 G millimeter-wave bands. The measured IL and RL at f0 are 1.09 and 18.02 dB, respectively. From 0 to 14.57 GHz and from 38.47 to 50 GHz, the measured SSL is over 20 dB. The total chip size is 2.72 × 2.35 mm, which is equivalent to 0.23 × 0.2 λ0, where λ0 is the free-space wavelength at f0 of 25.85 GHz. The zoomed-in view of the passband transmission coefficient of the second-order LN-based millimeter-wave BPF chip is shown in Supplementary Fig. 2b.

Fig. 3: Photograph and results of second-order LN-based millimeter-wave BPF chip.
Fig. 3: Photograph and results of second-order LN-based millimeter-wave BPF chip.
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a Photograph of a second-order LN-based millimeter-wave BPF chip. b Simulated and measured S parameters. c Simulated and measured group delay. d Measured minimum IL varies with temperature

Figure 3c presents the group delay of the fabricated second-order LN-based millimeter-wave BPF chip. The simulated maximum group delay is 91 ps, while the measured maximum group delay is 129 ps. A cryogenic probe station with a vacuum system and a temperature control system has been applied for high- and low-temperature measurements. A photograph of the applied cryogenic probe station in the measurement is shown in Supplementary Fig. 3a. Figure 3d presents the measured minimum IL of the fabricated second-order LN-based millimeter-wave BPF chip from −150 °C to 150 °C. It can be observed that the IL is in proportion to the temperature, and the minimum IL at −150 °C is 0.22 dB, which is also a record-breaking value for filtering loss. The measured transmission coefficient and its zoomed-in view at the passband of the fabricated second-order LN-based millimeter-wave BPF chip at −150 °C are shown in Supplementary Fig. 3b. This characterization can reveal the potential of the proposed LN-based millimeter-wave BPFs for the low-temperature quantum information.

Fourth-order LN-based millimeter-wave BPF chip

Based on the above second-order LN-based millimeter-wave BPF chip, a CPW dual-mode resonator is added to construct the proposed fourth-order LN-based millimeter-wave BPF chip. Figure 4a presents the whole structure of the CPW dual-mode resonator. By using the even-odd-mode analysis, a CPW half-wavelength resonator, and a CPW quarter-wavelength resonator are obtained at the even mode and odd mode, respectively. Figure 4b, c presents the schematic diagram of CPW half-wavelength resonator at the even mode and the schematic diagram of CPW quarter-wavelength resonator at the odd mode, respectively. The resonant frequency of the CPW quarter-wavelength resonator at the odd mode can be tuned by the length L1, while the resonant frequency of the CPW half-wavelength resonator at the even mode can be independently tuned by the length L2.

Fig. 4: CPW dual-mode resonator, even-odd-mode resonators, structure and simulation of fourth-order LN-based millimeter-wave BPF chip.
Fig. 4: CPW dual-mode resonator, even-odd-mode resonators, structure and simulation of fourth-order LN-based millimeter-wave BPF chip.
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a CPW dual-mode resonator. b Even-mode resonator. c Odd-mode resonator. d Top view and perspective view of fourth-order LN-based millimeter-wave BPF chip. The optimized dimensions are: L1 = 3.68, L2 = 0.65, L3 = 0.94, L4 = 0.1, L5 = 1.2, L6 = 0.87, W1 = 2.35, W2 = 0.35, W3 = 0.15, W4 = 0.05, W5 = 0.25, W6 = 0.25, g1 = 0.475, g2 = 0.01, t = 0.015, and h = 0.15, all in mm. e The f0 of fourth-order LN-based millimeter-wave BPF chip adjusted by length L3 and L5. f The passband bandwidth of fourth-order LN-based millimeter-wave BPF chip adjusted by gap g1

Figure 4d presents the top view and perspective view of the proposed fourth-order LN-based millimeter-wave BPF chip. The coupling scheme of the fourth-order LN-based millimeter-wave BPF chip is shown in Supplementary Fig. 4. Figure 4e presents the f0 of the fourth-order LN-based millimeter-wave BPF chip tuned by the lengths L3 and L5. When the lengths L3 and L5 are increased, the f0 is reduced. Figure 4f presents the passband bandwidth of the fourth-order LN-based millimeter-wave BPF chip adjusted by the coupling gap g1. When the gap g1 is increased, the bandwidth of the passband is reduced. As a result, the f0 and bandwidth of the proposed fourth-order LN-based millimeter-wave BPF chip can be independently controlled.

Figure 5a presents a photograph of the fabricated fourth-order LN-based millimeter-wave BPF chip, and two 50-ohm GSG probes with a pitch of 0.6 mm are connected to the CPW ports for measurements. The size comparison photograph of the fabricated fourth-order LN-based millimeter-wave BPF chip with a coin is shown in Supplementary Fig. 5. Figure 5b presents the simulated and measured S parameters of the fabricated fourth-order LN-based millimeter-wave BPF chip. The simulated f0 is 32 GHz, and the 3-dB bandwidth is 23.55–40.45 GHz (52.8%). The simulated IL and RL at f0 are 0.98 and 15.39 dB, respectively. From 0 to 17.16 GHz and from 45.6 to 50 GHz, the simulated SSL is over 20 dB. The measured f0 is 32.16 GHz, and the 3-dB bandwidth is 23.24–41.08 GHz (55.5%), which can cover the n257, n258, and n260 5 G millimeter-wave bands. The measured IL and RL at f0 are 1.14 and 35.96 dB, respectively. From 0 to 18.09 GHz and from 46.42 to 50 GHz, the measured SSL is over 20 dB. The total chip size is 3.68 × 2.35 mm, which is equivalent to 0.39 × 0.25 λ0, where λ0 is the free-space wavelength at f0 of 32.16 GHz. The zoomed-in view of the transmission coefficient at the passband of the fourth-order LN-based millimeter-wave BPF chip is shown in Fig. 5c. Figure 5d presents the group delay of the fabricated fourth-order LN-based millimeter-wave BPF chip. The simulated maximum group delay is 121 ps, while the measured maximum group delay is 142 ps. Thus, the obtained small group delay of the proposed LN-based millimeter-wave BPFs can fulfill the requirements of high-speed millimeter-wave communications. The fabrication tolerance and copper surface roughness are the main reasons for small discrepancies between simulated and measured results.

Fig. 5: Photograph and results of fourth-order LN-based millimeter-wave BPF chip.
Fig. 5: Photograph and results of fourth-order LN-based millimeter-wave BPF chip.
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a Photograph of a fourth-order LN-based millimeter-wave BPF chip. b Simulated and measured S parameters of fourth-order LN-based millimeter-wave BPF chip. c Zoomed-in view of transmission coefficient at the passband. d Simulated and measured group delay

Table 1 compares the performance of the presented second-order and fourth-order LN-based millimeter-wave BPF chips with other state-of-the-art millimeter-wave BPFs by using the MEMS, PCB, LTCC, and IPD process technologies. The acoustic millimeter-wave BPFs show small size but have large IL and small SSL. Generally, the electromagnetic millimeter-wave BPFs based on PCB and LTCC technologies have large size and large IL. The IPD-based millimeter-wave BPFs show small size but have large IL. Moreover, millimeter-wave BPFs based on LTCC and IPD technologies suffer from high cost. It can be observed that our presented second-order and fourth-order LN-based millimeter-wave BPF chips have realized optimal balance among filter size, frequency selectivity, and cost. Our proposed LN-based millimeter-wave BPF chips with ultra-small size, low passband IL, high selectivity, and low cost will be promising for next-generation millimeter-wave wireless communications, sensing, imaging, and quantum information.

Table 1 Comparisons with some reported state-of-the-art millimeter-wave BPFs
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Conclusion

The LN crystal film offers a versatile platform that integrates photonic, acoustic, and electromagnetic functionalities. This multifunctionality, combined with its unique properties, makes LN an ideal material for developing high-performance millimeter-wave BPFs. Three critical advantages make LN well-suited for millimeter-wave filter applications. Firstly, as a high-K material, the large permittivity of LN is beneficial for realizing small sizes. Secondly, the LN has a low dielectric loss, which can result in high-Q resonators and high-selectivity filters. Thirdly, the ease of fabrication and low cost of LN will facilitate the mass production of our proposed LN-based millimeter-wave BPF chips. Second-order and fourth-order LN-based millimeter-wave BPF chips are presented for narrowband and wideband millimeter-wave applications, respectively. The fabrication process, which has high production efficiency, a short processing cycle, and low cost, is well suited for mass production of the LN-based millimeter-wave BPF chips. Furthermore, taking advantage of the high-precision MEMS fabrication technology, the working frequency of LN-based filter chips can be extended from the millimeter-wave spectrum to the terahertz-wave spectrum. Our proposed LN-based BPFs fulfill the critical demands of millimeter-wave wireless communications, sensing, imaging, and emerging quantum information systems, paving the way for scalable, multi-physical integrated circuits.

Methods

High-K single-crystal LN

The LN is a high-K single crystal and an anisotropic crystal. The permittivity matrices for any orientations and cuts of LN can be obtained by51

$$\tilde{\varepsilon }=a\cdot {\varepsilon }_{Z}\cdot {a}^{t}$$
(3)

Where a is the transformation matrix, and εZ is the permittivity matrix of Z-cut oriented LN with ε11 = 45, ε22 = 45, ε33 = 29. The high permittivity of LN is critical to realizing the LN-based millimeter-wave filter chips with small sizes. The Czochralski method is applied to produce the single-crystal LN. The ease of fabrication will facilitate the mass production of LN-based millimeter-wave BPF chips.

Cutoff frequency of high-order modes

The high permittivity, thick substrate, and high frequency are three major factors in the excitation of high-order modes, including the transverse magnetic (TM) and transverse electric (TE) modes. The high-order modes in the homogeneous dielectric substrate have been investigated52. The cutoff frequencies of high-order modes are expressed as

$${f}_{c}({{\rm{TM}}}_{{\rm{n}}})=\frac{{\rm{n}}c}{2h\sqrt{{\varepsilon }_{r}-1}}$$
(4)
$${f}_{c}({{\rm{TE}}}_{{\rm{m}}})=\frac{(2{\rm{m}}-1)c}{4h\sqrt{{\varepsilon }_{r}-1}}$$
(5)

where n = 0, 2, 4, … and m = 1, 3, 5, … represent the mode order, while the c and h represent the free-space speed of light and the thickness of the substrate, respectively. For the LN with anisotropic permittivity, the above Eqs. (4) and (5) remain valid for analysis. As the TM0 mode has zero cutoff frequency, the TE1 mode is the mainly concerned high-order mode.

LN thickness optimization

For the TE1 mode, the critical height is expressed as

$${h}_{c}({{\rm{TE}}}_{1})=\frac{c}{4{f}_{c}({{\rm{TE}}}_{1})\sqrt{{\varepsilon }_{r}-1}}$$
(6)

The cutoff frequency of the TE1 mode needs to be far away from the desired passband of the proposed LN-based millimeter-wave BPF chips. Here, we let the TE1 mode have the cutoff frequency of 75 GHz and εr = 45, and then the calculated critical thickness of LN is 150.8 μm. To increase the cutoff frequency of TE1 mode, the LN thickness needs to be reduced. However, the reduced LN thickness leads to an increased size of BPF chips. Taking a tradeoff between the cutoff frequency of TE1 mode and the size, the thickness of the applied 128° Y-cut LN is determined as 150 μm.

Chips fabrication

The MEMS fabrication technology with high precision is applied to fabricate the proposed LN-based millimeter-wave BPF chips. Figure 6 presents the fabrication process flow of our LN-based millimeter-wave BPF chips. Firstly, the 128° Y-cut LN wafer with a thickness of 150 μm and a mask of designed filters are prepared. Secondly, a sputterer is applied to deposit 20-nm titanium as the adhesive layer and then 100-nm copper as the seed layer on one side of the LN wafer. Thirdly, a spin coater is applied to coat a layer of photoresist (PR) with a thickness much larger than the skin depth of copper at the working frequency band. Fourthly, the photolithography is applied to transfer patterns on the PR by using the prepared mask, and then the patterns are created after the development process. Fifthly, considering the intrinsic stress and cost of the sputtered metal, the electroplating of copper is carried out, and the copper thickness should be much larger than the skin depth of electromagnetic waves.

Fig. 6: Fabrication process flow of LN-based millimeter-wave BPF chips.
Fig. 6: Fabrication process flow of LN-based millimeter-wave BPF chips.
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The fabrication process with high production efficiency, short processing cycle, and low cost is well suited for mass production of the LN-based millimeter-wave BPF chips

At the frequency of 30 GHz, the skin depth of copper is 0.38 μm. The thickness of copper without the cover of PR is increased to around the thickness of PR which is much larger than 0.38 μm. Finally, the acetone, copper etchant, and titanium etchant are applied to remove the PR, 100-nm copper seed layer, and 20-nm titanium adhesive layer, respectively. The wet etching of copper can cause lateral etching, but the etching thickness is a little more than 100 nm which is small enough and shall not cause significant performance degradation. The fabrication process, which has high production efficiency, a short processing cycle, and low cost, is well suited for mass production of our proposed LN-based millimeter-wave BPF chips.