PhD Thesis Arne Lüker final version V4 - Cranfield University

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esonance frequency [GHz] [MHz] 100 10 1 NCD 2 µm PZT 2 µm 166 Appendix A: PZT actuated Diamond Cantilever Technology PZT 0.5 µm/ NCD 2 µm 0,1 Al/PZT/Pt/NCD (simulated) 0,01 Al PZT Pt NCD 1E-3 10 100 cantilever length [µm] the resonance frequency by only 15 %. Adding the metallization layer will not cause any noticeable additional degradation. A.2.3 Cantilever deflection When applying an electrical field across the piezoelectric film, the strain generated between the piezoelectric film and the carrier substrate leads to a bending moment, which can either cause a deflection of the beam or can generate a force onto a base plate after the air gap is closed (see Fig. A3). The Data of the bending moment, deflection and force respectively can be obtained from Eq. A2 and A3 [4]: PZT Pt NCD PZT/Pt/NCD (simulated) Fig. A2: Calculated resonance frequencies (Eq. A1) of single layer cantilevers of 2.0 µm PZT and NCD and multilayer stacks of 0.5 µm PZT / 2.0 µm NCD. Also plotted are three points for the simulation of three complete Al/PZT/Pt/NCD stacks of 50, 100, and 590 µm length with thicknesses as mentioned in the text; for Young’s moduli see Table A1. z y x w tNCD tPZT electrodes NCD PZT base plate g ( 1+ B) 2 2 3L 2AB V δ = ⋅ ⋅ d (Eq. A2) 2 4 2t A B + 2A 2 3 31 ( 2B + 3B + 2B ) + 1 tPZT base plate Fig. A3: Operation of PZT/NCD unimorph. Applied electrical load induces cantilever bending until an initial airgap (g) towards a base plate is closed (δ=g); for even higher loads a force (F) onto the base plate is generated. δ=g
Sol-Gel derived Ferroelectric Thin Films for Voltage Tunable Applications 3wt E 2AB V = , (Eq. A3) 8L 2 F PZT ⋅ ⋅ d31 ( AB + 1)( 1+ B) tPZT where L, t, w are the cantilever length, thickness (tPZT + tdi), width, d31 the transversal piezoelectric coefficient, V the applied voltage, EPZT the Young’s modulus of the piezoelectric layer, A = Edi /EPZT the ratio of the Young’s moduli of diamond and PZT, and B = tdi /tPZT the ratio of the layer thicknesses, respectively. As actuator in a switch application, in the quiescent condition (without external electrical field) the switch is typically in the open condition and the cantilever separated from the base plate contact by an airgap. A force onto the base is therefore generated only after the cantilever has touched the base plate and the deflection is equal to the airgap. The diagram in Fig. A4 shows a calculation of the generated force for a 0.2 µm airgap as function of applied voltage (cantilever data: tip force [µN] 0.5 µm PZT on 2.0 µm NCD, width = 6 µm). It can be observed that the force increases for shorter cantilevers up to a maximum; for very short beams, where the maximum applicable field (~240 kV/cm; determined by device failure) results in a voltage which is to low to close the airgap, no contact force can be generated. 20 18 16 14 12 10 8 6 4 2 10 V 8 V 6 V 4 V 2 V 0 10 100 1000 cantilever length [µm] Fig. A4: Calculated tip contact force of PZT/NCD unimorph depending on beam length for different applied voltages (using equations (1) and (2)). 167
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Sol-Gel derived Ferroelectric Thin
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Table of Content Introduction and M
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Intensity [arb. Units] (g) (f) (e)
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Relative diel. diel. constant Const
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Intensity [arb. Units] Intensity [a
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PhD Thesis Arne Lüker final version V4 - Cranfield University

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