Stress Suppression Design for Radiofrequency Microelectromechanical System Switch Based on a Flexible Substrate

A novel stress suppression design for flexible RF MEMS switches has been presented and demonstrated through theoretical and experimental research to isolate the stress caused by substrate bending. An RF MEMS switch with an S-shaped microspring structure was fabricated by the two-step etching process as a developmental step toward miniaturization and high reliability. The RF MEMS switches with an S-shaped microspring exhibited superior microwave performance and stable driving voltage under different substrate curvatures compared to the conventional non-microspring switches, demonstrating that the bending stress is successfully suppressed by the S-shaped microspring and the island structure. Furthermore, this innovative design could be easily extended to other flexible devices.


Introduction
Recently, liquid crystal polymer (LCP) based devices have been extensively applied to the field of communications [1][2][3][4], radar [5][6][7][8], wearable devices [9][10][11][12], biomedical applications [13][14][15][16] and sensors [17][18][19][20], benefiting from their inherent flexibility and improved electrical material properties.As one of the common RF devices, an RF MEMS switch is indispensable in an RF system.We have presented the multi-physical modeling of bending characteristics to predict the drift of the performance with substrate bending in previous works [21][22][23].However, it is a fact that the performance of the flexible switch is deteriorated because it is affected by the bending stress when it is conformed to a curved surface.It is critical to design a low packaging stress structure for keeping the substrate as flat as possible under bending conditions.
Many methods have been reported to reduce the packaging stress.In 2015, Schröder S et al. proposed a stress minimized method by double-sided wire bonding [24].However, double-sided wire bonding is too complicated for mass production.In 2016, Yongcun Hao et al. presented a circular disk with eight L-shaped elastic beams to isolate the stress from out-of-plane deformation based on the silicon substrate, but this stress isolation structure cannot be directly migrated to substrates other than the SOI substrate [25].In 2019, Bowen Xing et al. reported a single center anchor packaging stress isolation structure for Si-based MEMS devices [26].Nevertheless, this structure was separated from the rigid substrate, which is detrimental to miniaturization and reliability.Few papers have focused on optimizing the bending stress for flexible devices, aiming at self-packaging, which is closely related to the performance of flexible devices.
In this paper, for the first time, we proposed an S-shaped microspring and an island structure to minimize the stress induced by substrate bending.The flexible LCP not only acts as a substrate to support the devices but also isolates stress from the substrate bending.The experimental results are consistent with the theoretical analysis and the S-shaped microspring switch successfully maintains superior microwave performance and stable driving voltage under different substrate curvatures compared to the conventional nonmicrospring switch, demonstrating that the innovative structure exhibits the function of suppressing stress from substrate bending.

Theoretical Model
As shown in Figure 1, for the conventional electrostatic double-clamped switch, the driving electrodes are symmetrically located on each side of the double-clamped beam.When the voltage is applied to the driving electrodes in the on state, the electrostatic force is generated between the beam and the driving electrodes.Hence, the beam bends downward under electrostatic force until it reaches the driving voltage.Meanwhile, the beam contacts with the CPW and shifts the switch to the off state.As the flexible substrate bends upward, the gap between the beam and the substrate decreases, generating stress and deteriorating the performance.
which is detrimental to miniaturization and reliability.Few papers have focused on opti mizing the bending stress for flexible devices, aiming at self-packaging, which is closely related to the performance of flexible devices.
In this paper, for the first time, we proposed an S-shaped microspring and an island structure to minimize the stress induced by substrate bending.The flexible LCP not only acts as a substrate to support the devices but also isolates stress from the substrate bend ing.The experimental results are consistent with the theoretical analysis and the S-shaped microspring switch successfully maintains superior microwave performance and stable driving voltage under different substrate curvatures compared to the conventional non microspring switch, demonstrating that the innovative structure exhibits the function o suppressing stress from substrate bending.

Theoretical Model
As shown in Figure 1, for the conventional electrostatic double-clamped switch, the driving electrodes are symmetrically located on each side of the double-clamped beam When the voltage is applied to the driving electrodes in the on state, the electrostatic force is generated between the beam and the driving electrodes.Hence, the beam bends down ward under electrostatic force until it reaches the driving voltage.Meanwhile, the beam contacts with the CPW and shifts the switch to the off state.As the flexible substrate bends upward, the gap between the beam and the substrate decreases, generating stress and deteriorating the performance.When the substrate is flat, the double-clamped beam is simplified into a stretched line to deduce the spring constant and the stretched line model is shown in Figure 2, where x1 to x1+a is the location of the right driving electrode and the q(x) is the load of the force When the electrostatic force is generated by applying voltage to the driving electrodes the spring constant k could be calculated by the superposition principle.When the substrate is flat, the double-clamped beam is simplified into a stretched line to deduce the spring constant and the stretched line model is shown in Figure 2, where x 1 to x 1+a is the location of the right driving electrode and the q(x) is the load of the force.When the electrostatic force is generated by applying voltage to the driving electrodes, the spring constant k could be calculated by the superposition principle.
where E is Young's modulus; I is the rotational inertia; and L, t and w are the length, thickness and width of the double-clamped beam, respectively.
When the substrate is flat, the double-clamped beam is simplified into a stretched line to deduce the spring constant and the stretched line model is shown in Figure 2, where x1 to x1+a is the location of the right driving electrode and the q(x) is the load of the force.When the electrostatic force is generated by applying voltage to the driving electrodes, the spring constant k could be calculated by the superposition principle.Considering that the driving electrodes are symmetrically located on each side of the beam, the driving voltage can be obtained by: where a is the closer distance between the beam and the driving electrodes and g is the distance between the beam and the driving electrodes.
When the residual stress of the beam is greater than the critical force, the beam would buckle.The variation of compressive force can be expressed as: where ε is the Poisson ratio and ∆L is the variation of the length of the beam.
When the substrate bends upward, the gap between the beam and driving electrodes decreases resulting from the deformation of the flexible substrate and the beam, which has a direct influence on the driving voltage.
As shown in Figure 3, L is the length of the beam, g is the initial gap between the beam and the substrate, and R is the radius of the flexible bending substrate and could be expressed by: Materials 2024, 17, x FOR PEER REVIEW 3 of 14 x a x x a x EI q z dz k q z L L z Lz z dz where E is Young's modulus; I is the rotational inertia; and L, t and w are the length, thickness and width of the double-clamped beam, respectively.Considering that the driving electrodes are symmetrically located on each side of the beam, the driving voltage can be obtained by: where  is the closer distance between the beam and the driving electrodes and g is the distance between the beam and the driving electrodes.
When the residual stress of the beam is greater than the critical force, the beam would buckle.The variation of compressive force can be expressed as: where  is the Poisson ratio and Δ is the variation of the length of the beam.When the substrate bends upward, the gap between the beam and driving electrodes decreases resulting from the deformation of the flexible substrate and the beam, which has a direct influence on the driving voltage.
As shown in Figure 3, L is the length of the beam, g is the initial gap between the beam and the substrate, and R is the radius of the flexible bending substrate and could be expressed by: The variation in the distance between the beam and the substrate is: The variation in the distance between the beam and the substrate is: If the beam remains flat when the substrate is bending, the variation in the distance between the beam and the substrate could be deduced by: Therefore, when the substrate is bending upward, the equation of the driving voltage could be further expressed by the following formula considering the influence from X ′ : Besides, when the substrate bends, the double-clamped beam deforms under the tensile stress from both the substrate and the beam.Therefore, the tensile force P under different bending curvatures could be deduced by: As shown in Figure 4, the beam would buckle when the tensile force P is less than the residual strain.Therefore, the symmetrical beam structure can be expressed by the deflection equation u(x) as: where l is the length of the sloping part and a is the angle between the sloping part and the flat part.Considering that it is relative to the tensile force P under different bending radius, the relationship of a and P could be expressed by: where a 0 is the maximum angle only caused by the residual stress, k a is the coefficient, and P 0 is the residual force.If the beam remains flat when the substrate is bending, the variation in the distance between the beam and the substrate could be deduced by: Therefore, when the substrate is bending upward, the equation of the driving voltage could be further expressed by the following formula considering the influence from X ′ : Besides, when the substrate bends, the double-clamped beam deforms under the tensile stress from both the substrate and the beam.Therefore, the tensile force P under different bending curvatures could be deduced by: As shown in Figure 4, the beam would buckle when the tensile force P is less than the residual strain.Therefore, the symmetrical beam structure can be expressed by the deflection equation u(x) as: where l is the length of the sloping part and a is the angle between the sloping part and the flat part.Considering that it is relative to the tensile force P under different bending radius, the relationship of a and P could be expressed by: where  is the maximum angle only caused by the residual stress, ka is the coefficient, and P0 is the residual force.By substituting the deflection equation into the revised driving voltage equation, the driving voltage under different bending radii without a substrate microspring can be obtained by: As shown in Figure 5, H is the thickness, B is the line width, and D is the gap width.For the S-shaped microspring, the spring constant in tension k s and vertical spring constant k v can be respectively expressed as: where E is the Young's modulus of the material, n is the number of the S-shaped unit and I ρ is the polar moment of inertia.
Materials 2024, 17, x FOR PEER REVIEW 5 of 14 By substituting the deflection equation into the revised driving voltage equation, the driving voltage under different bending radii without a substrate microspring can be obtained by: As shown in Figure 5, H is the thickness, B is the line width, and D is the gap width.For the S-shaped microspring, the spring constant in tension ks and vertical spring constant kv can be respectively expressed as:  ) where E is the Young's modulus of the material, n is the number of the S-shaped unit and  is the polar moment of inertia.
The variation of the S-shape microspring length Δ can be obtained by: where  is the initial length of the S-shape microspring.Therefore, the stress of the S-shape microspring T can be calculated by: The variation of the S-shape microspring length ∆L s can be obtained by: where L s is the initial length of the S-shape microspring.Therefore, the stress of the S-shape microspring T can be calculated by:

Materials and Tools
The material of the substrate is single-sided copper-clad LCP and the functional layers such as the CPW line, anchor and beam are made up of Au.
The finite element method by COMSOL 6.2 software is used to analyze the mechanisms of the flexible MEMS switches with the non-microspring and the S-shaped microspring.Ansys Electronics Desktop 2022 R1 is used to simulate the microwave characteristics of the two types of switches.
The different bending curvature frames of 0 m −1 , 20.0 m −1 , 22.2 m −1 , 25.0 m −1 , and 28.6 m −1 are designed to provide the test conditions.The driving voltage and S parameters are measured by an adjustable DC source (UNIT, Dongguan, China), a vector network analyzer (Keysight Technologies, Santa Rosa, CA, USA), and a probe station (Cascade Microtech, Beaverton, OR, USA) with two 150 µm pitch G/S/G probes.

Design and Simulation
The RF MEMS switch with an S-shaped microspring structure, which has a low stress package, is designed as in Figure 6.The two edges where the pads are located are fixed and attached to the bending curvature frame, enabling the structure to bend along the CPW.The four cavities create four S-shaped microsprings in the substrate, which turn the central part of the substrate into an island structure.The spring constant of the S-shaped microspring is lower than that of the central island structure.Therefore, the deformation in bending is mainly centralized in the S-shaped microspring when the substrate is curved, which keeps the central island structure almost flat under different curvatures.Thus, the effect of substrate curvature on the switch is reduced, significantly maintaining the outstanding switch performance.
The finite element method by COMSOL 6.2 software is used to analyze the mechanisms of the flexible MEMS switches with the non-microspring and the S-shaped microspring.Ansys Electronics Desktop 2022 R1 is used to simulate the microwave characteristics of the two types of switches.
The different bending curvature frames of 0 m −1 , 20.0 m −1 , 22.2 m −1 , 25.0 m −1 , and 28.6 m −1 are designed to provide the test conditions.The driving voltage and S parameters are measured by an adjustable DC source (UNIT, Dongguan, China), a vector network analyzer (Keysight Technologies, Santa Rosa, CA, USA), and a probe station (Cascade Microtech, Beaverton, OR, USA) with two 150 µm pitch G/S/G probes.

Design and Simulation
The RF MEMS switch with an S-shaped microspring structure, which has a low stress package, is designed as in Figure 6.The two edges where the pads are located are fixed and attached to the bending curvature frame, enabling the structure to bend along the CPW.The four cavities create four S-shaped microsprings in the substrate, which turn the central part of the substrate into an island structure.The spring constant of the S-shaped microspring is lower than that of the central island structure.Therefore, the deformation in bending is mainly centralized in the S-shaped microspring when the substrate is curved, which keeps the central island structure almost flat under different curvatures.Thus, the effect of substrate curvature on the switch is reduced, significantly maintaining the outstanding switch performance.The low stress package size is designed to be 6 mm × 6 mm and the geometric parameters of the double-clamped beam switch are listed in Table 1.The low stress package size is designed to be 6 mm × 6 mm and the geometric parameters of the double-clamped beam switch are listed in Table 1.As the curvature rises, the stress of the switch is increased and the gap between the beam and the driving electrode is reduced.The driving voltage is related to the stress and the gap, and the overall effect on the driving voltage is decreasing.The simulated driving voltages of the switches with a non-microspring and an S-shaped microspring versus the curvature are shown in Figure 7.For a non-microspring switch, the driving voltage declines dramatically.However, the variation of the S-shaped microspring is relatively flat, demonstrating that the stress and the gap of the switch are nearly unchanged.Therefore, the S-shaped microspring and the island structure indeed efficiently reduce the stress caused by the substrate bending, which is consistent with the theoretical predictions.
Width of the pad 400 Length of the pad 2225 As the curvature rises, the stress of the switch is increased and the gap between beam and the driving electrode is reduced.The driving voltage is related to the stress the gap, and the overall effect on the driving voltage is decreasing.The simulated driv voltages of the switches with a non-microspring and an S-shaped microspring versus curvature are shown in Figure 7.For a non-microspring switch, the driving voltage clines dramatically.However, the variation of the S-shaped microspring is relatively demonstrating that the stress and the gap of the switch are nearly unchanged.Theref the S-shaped microspring and the island structure indeed efficiently reduce the st caused by the substrate bending, which is consistent with the theoretical predictions.As shown in Figure 8, with the increase of the curvature, the simulated return los and insertion loss S21 of the switch with the non-microspring are continuously degrad However, since the gap of the switch with the S-shaped microspring barely changes, S-parameters of different curvatures almost coincide with the curvature of 0 m −1 as sho in Figure 9.As shown in Figure 8, with the increase of the curvature, the simulated return loss S 11 and insertion loss S 21 of the switch with the non-microspring are continuously degraded.However, since the gap of the switch with the S-shaped microspring barely changes, the S-parameters of different curvatures almost coincide with the curvature of 0 m −1 as shown in Figure 9.
According to Equation ( 6), as the curvature increases, the gap of the non-microspring switch between the beam and the substrate reduces, leading to the deterioration in microwave performance.The S-shaped microspring keeps the central island structure flat under different curvatures and reduces the stress caused by the substrate bending, maintaining the high microwave performance.Hence, the simulation results are consistent with the tendency from the theoretical analysis.As the curvature rises, the stress of the switch is increased and the gap between the beam and the driving electrode is reduced.The driving voltage is related to the stress and the gap, and the overall effect on the driving voltage is decreasing.The simulated driving voltages of the switches with a non-microspring and an S-shaped microspring versus the curvature are shown in Figure 7.For a non-microspring switch, the driving voltage declines dramatically.However, the variation of the S-shaped microspring is relatively flat, demonstrating that the stress and the gap of the switch are nearly unchanged.Therefore, the S-shaped microspring and the island structure indeed efficiently reduce the stress caused by the substrate bending, which is consistent with the theoretical predictions.As shown in Figure 8, with the increase of the curvature, the simulated return loss S11 and insertion loss S21 of the switch with the non-microspring are continuously degraded.However, since the gap of the switch with the S-shaped microspring barely changes, the S-parameters of different curvatures almost coincide with the curvature of 0 m −1 as shown in Figure 9.According to Equation ( 6), as the curvature increases, the gap of the non-microspring switch between the beam and the substrate reduces, leading to the deterioration in microwave performance.The S-shaped microspring keeps the central island structure flat under different curvatures and reduces the stress caused by the substrate bending, maintaining the high microwave performance.Hence, the simulation results are consistent with the tendency from the theoretical analysis.
The simulation results of the stress distribution are shown in Figure 10.The stress of the non-microspring structure is concentrated in the switch.However, for the S-shaped microspring structure, the stress is centralized in the S-shaped microspring, effectively reducing the bending influence on the switch.

Fabrication
The fabrication process of the switch with an S-shaped microspring structure is shown in Figure 11.The microspring structures are firstly etched by laser and then bonded to a rigid substrate by temporary bonding to guarantee the substrate's flatness [27].After that, the CPW line is formed by traditional lithography, sputtering, plating, and etching.The photoresist is patterned on the CPW line to act as a sacrificial layer and could easily be removed in the following steps.Afterward, the 2 µm thick beam is fabricated on the The simulation results of the stress distribution are shown in Figure 10.The stress of the non-microspring structure is concentrated in the switch.However, for the S-shaped microspring structure, the stress is centralized in the S-shaped microspring, effectively reducing the bending influence on the switch.According to Equation ( 6), as the curvature increases, the gap of the non-microsprin switch between the beam and the substrate reduces, leading to the deterioration in micr wave performance.The S-shaped microspring keeps the central island structure flat und different curvatures and reduces the stress caused by the substrate bending, maintainin the high microwave performance.Hence, the simulation results are consistent with th tendency from the theoretical analysis.
The simulation results of the stress distribution are shown in Figure 10.The stress the non-microspring structure is concentrated in the switch.However, for the S-shape microspring structure, the stress is centralized in the S-shaped microspring, effective reducing the bending influence on the switch.

Fabrication
The fabrication process of the switch with an S-shaped microspring structure shown in Figure 11.The microspring structures are firstly etched by laser and then bonde to a rigid substrate by temporary bonding to guarantee the substrate's flatness [27].Aft that, the CPW line is formed by traditional lithography, sputtering, plating, and etchin The photoresist is patterned on the CPW line to act as a sacrificial layer and could easi be removed in the following steps.Afterward, the 2 µm thick beam is fabricated on th

Fabrication
The fabrication process of the switch with an S-shaped microspring structure is shown in Figure 11.The microspring structures are firstly etched by laser and then bonded to a rigid substrate by temporary bonding to guarantee the substrate's flatness [27].After that, the CPW line is formed by traditional lithography, sputtering, plating, and etching.The photoresist is patterned on the CPW line to act as a sacrificial layer and could easily be removed in the following steps.Afterward, the 2 µm thick beam is fabricated on the organic sacrificial layer by optimizing the plating time, plating current density, and plating electrolyte to achieve a good elasticity modulus.Next, the substrate microspring structures could be formed by backside wetting etching.At last, the sample is debonded and the sacrificial layer is removed by wetting treatment combined with supercritical drying.Meanwhile, the profile of the beam is kept and the fabrication of the switch is finished.Optical images of the two types of switches are shown in the Figure 12.
Materials 2024, 17, x FOR PEER REVIEW 9 of 14 organic sacrificial layer by optimizing the plating time, plating current density, and plating electrolyte to achieve a good elasticity modulus.Next, the substrate microspring structures could be formed by backside wetting etching.At last, the sample is debonded and the sacrificial layer is removed by wetting treatment combined with supercritical drying.Meanwhile, the profile of the beam is kept and the fabrication of the switch is finished.
Optical images of the two types of switches are shown in the Figure 12.

Results and Discussion
The measurement setup for testing the fabricated switches is shown in Figure 13.The switch is conformed to the test frame to measure the driving and microwave performance under different substrate bending conditions.organic sacrificial layer by optimizing the plating time, plating current density ing electrolyte to achieve a good elasticity modulus.Next, the substrate microsp tures could be formed by backside wetting etching.At last, the sample is deb the sacrificial layer is removed by wetting treatment combined with supercrit Meanwhile, the profile of the beam is kept and the fabrication of the switch Optical images of the two types of switches are shown in the Figure 12.

Results and Discussion
The measurement setup for testing the fabricated switches is shown in

Results and Discussion
The measurement setup for testing the fabricated switches is shown in Figure 13.The switch is conformed to the test frame to measure the driving and microwave performance under different substrate bending conditions.
The measured and calculated driving voltages of the switch with the non-microspring structure are shown in Figure 14.The two curves show the same variation trend that the driving voltage decreases as the substrate curvature increases since the gap between the beam and driving electrodes are dramatically reduced.Meanwhile, the measured results are in satisfactory agreement with the calculated results, within an error of 16%.The measured and calculated driving voltages of the switch with the non-microspring structure are shown in Figure 14.The two curves show the same variation trend that the driving voltage decreases as the substrate curvature increases since the gap between the beam and driving electrodes are dramatically reduced.Meanwhile, the measured results are in satisfactory agreement with the calculated results, within an error of 16%.The measured driving voltages of switches with a non-microspring and an S-shaped microspring are shown in Figure 15.The non-microspring switch suffers the whole bending effect, and thus the driving voltage drops from 94 V to 0 V when the substrate curvature rises from 0 m −1 to 28.6 m −1 .However, the S-shaped microspring switch has less variation compared to the conventional non-microspring switch, decreasing from 60 V to 40 V with a substrate curvature range of 0 m −1 to 28.6 m −1 .Therefore, the gap of the S-shaped microspring switch is almost unaffected by the substrate curvature, confirming that the Sshaped microspring and the island structure are efficient in suppressing the bending stress.The measured and calculated driving voltages of the switch with the non-microspring structure are shown in Figure 14.The two curves show the same variation trend that the driving voltage decreases as the substrate curvature increases since the gap between the beam and driving electrodes are dramatically reduced.Meanwhile, the measured results are in satisfactory agreement with the calculated results, within an error of 16%.The measured driving voltages of switches with a non-microspring and an S-shaped microspring are shown in Figure 15.The non-microspring switch suffers the whole bending effect, and thus the driving voltage drops from 94 V to 0 V when the substrate curvature rises from 0 m −1 to 28.6 m −1 .However, the S-shaped microspring switch has less variation compared to the conventional non-microspring switch, decreasing from 60 V to 40 V with a substrate curvature range of 0 m −1 to 28.6 m −1 .Therefore, the gap of the S-shaped microspring switch is almost unaffected by the substrate curvature, confirming that the Sshaped microspring and the island structure are efficient in suppressing the bending stress.The measured driving voltages of switches with a non-microspring and an S-shaped microspring are shown in Figure 15.The non-microspring switch suffers the whole bending effect, and thus the driving voltage drops from 94 V to 0 V when the substrate curvature rises from 0 m −1 to 28.6 m −1 .However, the S-shaped microspring switch has less variation compared to the conventional non-microspring switch, decreasing from 60 V to 40 V with a substrate curvature range of 0 m −1 to 28.6 m −1 .Therefore, the gap of the S-shaped microspring switch is almost unaffected by the substrate curvature, confirming that the Sshaped microspring and the island structure are efficient in suppressing the bending stress.
As shown in Figure 16a, with the increasing curvature, the average measured return loss S 11 of the non-microspring switch has an obvious degradation from −30 dB to −13 dB.When the bending curvature is 28.6 m −1 , the S 11 increases by at least 13 dB compared to the initial state.The measured insertion loss S 21 under different curvatures is shown in Figure 16b and the average S 21 is degraded by 1.17 dB, from −1.58 dB to −2.75 dB.
The S parameters of the S-shaped microspring switch are shown in Figure 17.With the increase of bending curvature from 0 m −1 to 28.6 m −1 , the average return loss S 11 deteriorates from −24 dB to −18 dB and the insertion loss S 21 is almost invariable.As a result, the fluctuation of the S-shaped microspring switch is lower than the non-microspring switch, validating that the bending stress is successfully suppressed by the S-shaped microspring and the island structure.As shown in Figure 16a, with the increasing curvature, the average measured return loss S11 of the non-microspring switch has an obvious degradation from −30 dB to −13 dB.When the bending curvature is 28.6 m −1 , the S11 increases by at least 13 dB compared to the initial state.The measured insertion loss S21 under different curvatures is shown in Figure 16b and the average S21 is degraded by 1.17 dB, from −1.58 dB to −2.75 dB.The S parameters of the S-shaped microspring switch are shown in Figure 17.With the increase of bending curvature from 0 m −1 to 28.6 m −1 , the average return loss S11 deteriorates from −24 dB to −18 dB and the insertion loss S21 is almost invariable.As a result, the fluctuation of the S-shaped microspring switch is lower than the non-microspring switch, validating that the bending stress is successfully suppressed by the S-shaped microspring and the island structure.As shown in Figure 16a, with the increasing curvature, the average measured return loss S11 of the non-microspring switch has an obvious degradation from −30 dB to −13 dB.When the bending curvature is 28.6 m −1 , the S11 increases by at least 13 dB compared to the initial state.The measured insertion loss S21 under different curvatures is shown in Figure 16b and the average S21 is degraded by 1.17 dB, from −1.58 dB to −2.75 dB.The S parameters of the S-shaped microspring switch are shown in Figure 17.With the increase of bending curvature from 0 m −1 to 28.6 m −1 , the average return loss S11 deteriorates from −24 dB to −18 dB and the insertion loss S21 is almost invariable.As a result, the fluctuation of the S-shaped microspring switch is lower than the non-microspring switch, validating that the bending stress is successfully suppressed by the S-shaped microspring and the island structure.The isolation S21 of the two switches with different bending curvatures in the off state are overlapping as shown in Figure 18.The results are independent of the substrate curvature, since the off state originates from the contact of the beam with the CPW.The isolation S 21 of the two switches with different bending curvatures in the off state are overlapping as shown in Figure 18.The results are independent of the substrate curvature, since the off state originates from the contact of the beam with the CPW.The isolation S21 of the two switches with different bending curvatures in the off state are overlapping as shown in Figure 18.The results are independent of the substrate curvature, since the off state originates from the contact of the beam with the CPW.The measured results are consistent with the simulated results.For the non-microspring switch, the average error of return loss between the measured and simulated results is within 8.9 dB and the error of insertion loss is 0.68 dB.Correspondingly, the average error of return loss and insertion loss for the S-shaped microspring switch is 4.5 dB and 0.24 dB, respectively.The characteristic impedance of the switch is not a precise 50 Ω, which is a factor causing an error of return loss and insertion loss.Furthermore, the initial height of the non-microspring switch beam is not 2 µm as expected due to the residual stress resulting from the fabrication process, which also affects the S-parameters.In general, the S-shaped microspring and the island structure effectively suppress the bending stress, ensuring the maintenance of an outstanding microwave performance and invariant driving voltage.The measured results are consistent with the simulated results.For the non-microspring switch, the average error of return loss between the measured and simulated results is within 8.9 dB and the error of insertion loss is 0.68 dB.Correspondingly, the average error of return loss and insertion loss for the S-shaped microspring switch is 4.5 dB and 0.24 dB, respectively.The characteristic impedance of the switch is not a precise 50 Ω, which is a factor causing an error of return loss and insertion loss.Furthermore, the initial height of the non-microspring switch beam is not 2 µm as expected due to the residual stress resulting from the fabrication process, which also affects the S-parameters.In general, the S-shaped microspring and the island structure effectively suppress the bending stress, ensuring the maintenance of an outstanding microwave performance and invariant driving voltage.

Conclusions
In conclusion, a low self-packaging stress method of producing a flexible RF MEMS switch is presented and verified by the theoretical and experimental results.Apart from being a substrate, the LCP also serves as a stress isolation through the S-shaped microspring and the island structure formed by the cavities.The calculated, simulated, and measured results are consistent with others, and the provided results demonstrate that the S-shaped microspring and the island structure effectively suppress the bending stress, resulting in superior microwave performance and stable driving voltage of the S-shaped microspring switch under different substrate curvatures compared to a conventional non-microspring switch.Hence, the stress suppression design proposed in this paper is a promising choice for the bending environment and is easy to extend to other flexible devices, showing enormous potential for device miniaturization and reliability.

Figure 1 .
Figure 1.A model of an electrostatic double-clamped switch.

Figure 2 .
Figure 2. Stretched line model of the double-clamped switch.

Figure 1 .
Figure 1.A model of an electrostatic double-clamped switch.

Figure 2 .
Figure 2. Stretched line model of the double-clamped switch.Figure 2. Stretched line model of the double-clamped switch.

Figure 2 .
Figure 2. Stretched line model of the double-clamped switch.Figure 2. Stretched line model of the double-clamped switch.

Figure 3 .
Figure 3.The two-dimension model of the double-clamped beam under the bending condition.

Figure 3 .
Figure 3.The two-dimension model of the double-clamped beam under the bending condition.

Figure 4 .
Figure 4.The 2D model of the beam without a spring structure under bending.Figure 4. The 2D model of the beam without a spring structure under bending.

Figure 4 .
Figure 4.The 2D model of the beam without a spring structure under bending.Figure 4. The 2D model of the beam without a spring structure under bending.

Figure 5 .
Figure 5.The 2D model of the S-shaped microspring.

Figure 5 .
Figure 5.The 2D model of the S-shaped microspring.

Figure 6 .
Figure 6.The design of the S-shaped microspring structure.

Table 1 .Figure 6 .
Figure 6.The design of the S-shaped microspring structure.

Table 1 .
Geometric parameters of the double-clamped beam switch.S-shape microspring 664 Length of the S-shape microspring 1015 Package size of the switch 6000 × 6000 Width of the pad 400 Length of the pad 2225

Figure 7 .
Figure 7.The simulated and calculated driving voltages of switches with non-microsprings an shaped microsprings as the substrate bending curvature increases.

Figure 8 .
Figure 8.The simulated results of the non-microspring switch in the on state.(a) Return loss S11 insertion loss S21.

Figure 7 .
Figure 7.The simulated and calculated driving voltages of switches with non-microsprings and S-shaped microsprings as the substrate bending curvature increases.

Figure 7 .
Figure 7.The simulated and calculated driving voltages of switches with non-microsprings and Sshaped microsprings as the substrate bending curvature increases.

Figure 8 .
Figure 8.The simulated results of the non-microspring switch in the on state.(a) Return loss S11; (b) insertion loss S21.

Figure 8 .Figure 9 .
Figure 8.The simulated results of the non-microspring switch in the on state.(a) Return loss S 11 ; (b) insertion loss S 21 .

Figure 9 .
Figure 9.The simulated results of the S-shaped microspring switch in the on state.(a) Return loss S 11 ; (b) insertion loss S 21 .

Figure 9 .
Figure 9.The simulated results of the S-shaped microspring switch in the on state.(a) Return lo S11; (b) insertion loss S21.
Fig switch is conformed to the test frame to measure the driving and microwave p under different substrate bending conditions.

Figure 12 .
Figure 12.An optical image of two types of switches.(a) A switch with a non-microspring structure; (b) a switch with an S-shaped microspring structure.

Figure 13 .
Figure 13.(a) The test circuit for the driving voltage and the microwave performance.(b) The measurement setup for testing the as-fabricated switches.

Figure 14 .
Figure 14.The measured and calculated driving voltage of a switch with a non-microspring structure.

Figure 13 .
Figure 13.(a) The test circuit for the driving voltage and the microwave performance.(b) The measurement setup for testing the as-fabricated switches.

Figure 13 .
Figure 13.(a) The test circuit for the driving voltage and the microwave performance.(b) The measurement setup for testing the as-fabricated switches.

Figure 14 .
Figure 14.The measured and calculated driving voltage of a switch with a non-microspring structure.

Figure 14 .
Figure 14.The measured and calculated driving voltage of a switch with a non-microspring structure.

Figure 15 .
Figure 15.The measured driving voltage of non-microspring and S-shaped microspring switches as the bending curvature increases.

Figure 16 .
Figure 16.The measured results of the non-microspring switch in the on state.(a) Return loss S11; (b) insertion loss S21.

Figure 15 .
Figure 15.The measured driving voltage of non-microspring and S-shaped microspring switches as the bending curvature increases.

Figure 15 .
Figure 15.The measured driving voltage of non-microspring and S-shaped microspring switches as the bending curvature increases.

Figure 16 .
Figure 16.The measured results of the non-microspring switch in the on state.(a) Return loss S11; (b) insertion loss S21.

Figure 16 .Figure 17 .
Figure 16.The measured results of the non-microspring switch in the on state.(a) Return loss S 11 ; (b) insertion loss S 21 .Materials 2024, 17, x FOR PEER REVIEW 12 of 14

Figure 17 .
Figure 17.The measured results of the S-shaped microspring switch in the on state.(a) Return loss S 11 ; (b) insertion loss S 21 .

Figure 17 .
Figure 17.The measured results of the S-shaped microspring switch in the on state.(a) Return loss S11; (b) insertion loss S21.

Figure 18 .
Figure 18.The isolation S21 of two types of switches in the off state.(a) the non-microspring switch; (b) the S-shaped microspring switch.

Figure 18 .
Figure 18.The isolation S 21 of two types of switches in the off state.(a) the non-microspring switch; (b) the S-shaped microspring switch.