A flexoelectric microelectromechanical system on silicon

Transcription

1 A flexoelectric microelectromechanical system on silicon Umesh Kumar Bhaskar, Nirupam Banerjee, Amir Abdollahi, Zhe Wang, Darrell G. Schlom, Guus Rijnders, and Gustau Catalan Supporting Information Figure S1 Schematic representation of the steps in the fabrication of all oxide flexoelectric cantilevers. Step 1: Lift-off patterning of the epitaxial oxide-heterostructures utilizing the pre- NATURE NANOTECHNOLOGY 1

2 patterned AlO x mask layer. Step 2: Patterning the top electrode layer. Step 3: Release of the freestanding devices by anisotropic substrate etching. Figure S2 X-Ray diffraction pattern of the perovskite heterostructures. ϕ-scan of the 101 STO is given as the inset confirming epitaxial growth. Comparison of paraelectric STO with ferroelectric PZT cantilevers The curvature vs voltage characteristic of STO cantilevers (Figure 3) is linear and not hysteretic. For comparison, we show below the curvature vs voltage of our flexoelectric STO cantilever, compared with equivalent measurements also done by us on a ferroelectric PZT bimorph cantilever (The PZT bimorph structure, was fabricated with a 75 nm thick PZT, 75 nm thick YSZ and 30 nm thick SRO for the top and bottom electrodes). The PZT cantilevers exhibit the typical butterfly hysteresis loops expected in ferroelectric materials, whereas the STO cantilevers display linear response with no hysteresis. The scatter of the points (from multiple cycles) is due to the slight drift of the signal over time. This drift of the signal is removed from the final response before Fourier filtering the displacement. 2 NATURE NANOTECHNOLOGY

3 SUPPLEMENTARY INFORMATION Figure S3. Variance of curvature with applied AC electric field for (a) 70 nm STO and (b) a 75 nm thick, ferroelectric PZT bimorph cantilever. The PZT bimorph structure also includes a layer of 75 nm thick YSZ to serve as the elastic layer. NATURE NANOTECHNOLOGY 3

4 Complete response,both filtered and unfiltered curvature measurement, of the nanocantilever at 100 KHz Figure S4 The unfiltered (d_ac), as well as, the Fourier-filtered first harmonic (Fh_d_ac) and second harmonic (Sh_d_ac) displacements, induced in the 16 x 40 um STO cantilever plate, are plotted as a function of the AC excitation of 1 V at 100 KHz. Estimation of the first resonance frequency of the cantilever The first resonance frequencies of a cantilever of length L (released length = 16 µm), width W (= 40 µm), thickness t (= 70 nm), with Young s modulus E (= 300 GPa), atomic density (ρ c = 5.12g/cm 3 ) is given as 1 4 NATURE NANOTECHNOLOGY

5 SUPPLEMENTARY INFORMATION Estimation of the static flexoelectric response from the dynamic response The static measurement of the device was not made because dynamic measurements allow the application of Fourier filtering techniques for filtering out noise, thereby increasing the accuracy of the measurement; the 1/f vibrational noise is maximum in static measurements and decreases at high frequencies. Nevertheless, here is no physical reason preventing static actuation and/or measurement, and the magnitude of the static flexoelectric response should be close to the dynamic flexoelectric response measured at 100 KHz. Experimentally, (Figure 3) we can see that the amplitude has already almost reached the DC asymptote at 100kHz. We can also calculate the static value corresponding to the extrapolation of our measurements to zero frequency. In order to estimate the static flexoelectric coefficient, we can fit the observed frequency dependence of the dynamic flexoelectric response (Figure 3) to the standard Lorentzian equation of a resonance peak (Eq 4-13 in ref 2 ): ( ) (1) [( ) ( ) ] The fit (see figure S5 below) yields a value for the static flexoelectric coefficient µ s = A/ ~ 3.9 nc/m, which is close to the dynamic flexoelectric coefficient µ= 4.1 nc/m, measured at 100 KHz. NATURE NANOTECHNOLOGY 5

6 Figure S5 The observed dynamic flexoelectric response µ(ω) as a function of the frequency (ω) is fit to equation 1 for the STO nano-cantilever at 1V excitation. Flexoelectric coefficient estimation at 10 KHz In order to demonstrate the stability of the measurements as a function of the frequency, we also include a complete curvature vs field measurement made at 10 KHz (more than a decade below the resonance frequency) and obtained similar curvatures and flexoelectric coefficients, as shown in figure S6 below. These measurements were made on a different cantilever, but with the same dimensions fabricated on the same chip. The obtained flexoelectric coefficient is 3.8 ± 0.15 nc/m at 10 KHz; this is very close to the calculated coefficient for the cantilever measured at 100 KHz, which illustrates also the robustness of the result and the relatively small sample to sample variability. 6 NATURE NANOTECHNOLOGY

7 SUPPLEMENTARY INFORMATION Figure S6 The first harmonic, flexoelectric curvature shows a linear variance when plotted as a function of the applied AC field at 10 KHz, more than one order of magnitude below the resonant frequency amplification. Web app for the comparison of piezoelectric and flexoelectric actuation We have also created a web-app to compare piezoelectric actuation and flexoelectric actuation for different geometric/material configurations. Equation 1 discussed in the manuscript is used for the calculation of displacement via flexoelectric actuation. The bimorph equation [Equation 3 in 3 is used for the estimating the displacement from piezoelectric actuation. It provides a simple yet useful tool for calculating design parameters for MEMS: 1. McFarland, A. W., Poggi, M. a, Bottomley, L. a & Colton, J. S. Characterization of microcantilevers solely by frequency response acquisition. J. Micromechanics Microengineering 15, (2005). 2. French, A. P. Vibrations and Waves: the M.I.T introductory physics series. CBS Publishers & Distributors 89 (1971). 3. Dekkers, M. et al. The significance of the piezoelectric coefficient d31eff determined from cantilever structures. J. Micromechanics Microengineering 23, (2013). NATURE NANOTECHNOLOGY 7

8 4. Doll, J. C., Petzold, B. C., Ninan, B., Mullapudi, R. & Pruitt, B. L. Aluminum nitride on titanium for CMOS compatible piezoelectric transducers. Journal of Micromechanics and Microengineering 20, (2009). 5. Wang, P., Du, H., Shen, S., Zhang, M. & Liu, B. Preparation and characterization of ZnO microcantilever for nanoactuation. Nanoscale Res. Lett. 7, 176 (2012). 8 NATURE NANOTECHNOLOGY