Self-Sealing Complex Oxide Resonators

Although 2D materials hold great potential for next-generation pressure sensors, recent studies revealed that gases permeate along the membrane-surface interface, necessitating additional sealing procedures. In this work, we demonstrate the use of free-standing complex oxides as self-sealing membranes that allow the reference cavity beneath to be sealed by a simple anneal. To test the hermeticity, we study the gas permeation time constants in nanomechanical resonators made from SrRuO3 and SrTiO3 membranes suspended over SiO2/Si cavities which show an improvement up to 4 orders of magnitude in the permeation time constant after annealing the devices. Similar devices fabricated on Si3N4/Si do not show such improvements, suggesting that the adhesion increase over SiO2 is mediated by oxygen bonds that are formed at the SiO2/complex oxide interface during the self-sealing anneal. Picosecond ultrasonics measurements confirm the improvement in the adhesion by 70% after annealing.

T g ∼ 45 • C. Once PPC is molded into the shape of the flake, the stack is cooled down to room temperature and the dome along with the flake is detached from the SiO 2 /Si. The flake is then transferred onto a prepatterned SiO 2 /Si device consisting cavities etched into SiO 2 /Si. Finally the flake is released above 60 • C leaving only the flake.

Prepatterend SiO 2 /Si
Dry thermal oxide of 285 nm, grown on highly doped (Si++) silicon is used as the substrate.
Vistec EBPG 5000+ is used to expose the cavity defined in 500 nm of AR-P 6200 positive e-beam resist. After exposure and development, the cavities are dry etched into the SiO 2 /Si using CHF 3 and Ar plasma until all the SiO 2 is removed. Remainder of AR-P 6200 is removed in PRS-3000 over night, rinsed and blow-dried. The substrates are further cleaned in O 2 plasma asher for 3 minutes. Similar procedure is employed for Si 3 N 4 /Si chips with 350 nm LPCVD grown Si 3 N 4 .

Annealing
The annealing takes place in ambient conditions on top of a VWR hot plate above 300 • C for 15 minutes to 1 hr.

Samples for ultra-fast acoustics
For the measurements of the acoustic boundary conditions using ultra-fast pump-probe method, separate samples need to be fabricated with metal layers deposited on top of the flakes. The metal layer is necessary to reflect the probe and absorb the pump to generate an acoustic pulse. Two  Figure S4 show the pressure response of the resonance frequency before and after annealing.
Before annealing, an average permeation time constant of τ p = 20.75 seconds is extracted. Individual τ p are listed in table S1. After annealing, this increases to τ p = 1.1×10 4 seconds.  Figure S5 show the pressure response of the resonance frequency before and after annealing.

STO device
Before annealing, an average permeation time constant of τ p = 13.87 seconds is extracted. Individual τ p are listed in table S2. After annealing, this increases to τ p = 1.2×10 5 seconds.

S.VI. EDX OF FREE-STANDING SRO
It is worth noting that the atomic force microscopy (AFM) profile of SRO flakes on SiO 2 /Si are 10.9 nm while the XRD data shown in the main text suggests a thickness of 6.3 nm. The discrepancy in the measured thicknesses between the two methods can be attributed to a few things.   Figure S8 shows an AFM image of the substrate after water etching. The bright left side still has SRO/SAO while the right side is the bare STO (001) substrate. Hints of terraces can still be seen on the bare STO after etching away the SAO, suggesting that most of the SAO is removed in water.

S.VIII. OPTICAL IMAGES AND AFM OF FLAKES NOT BEING PICKED UP BY POLYMER
In this section, we provide an additional evidence for the improved adhesion of complex oxide flakes on SiO 2 upon annealing. In Figs. S9 and S10, we compare the maneuverability of nonannealed and annealed SRO flakes, respectively. In Fig. S9, SRO flake on a dummy SiO 2 is picked up using a standard polycarbonate/PDMS dome technique 3,5 . It can be observed that the non-annealed SRO flakes are easily picked up from the original dummy SiO 2 and transferred to a patterned SiO 2 /Si. However, the same method used on annealed SRO flakes is unable to detach the flakes from the SiO 2 /Si substrate. Figure S10

S.IX. AFM OF FLAKES
In this section we use atomic force microscopy (AFM) to inspect SRO flakes before and after annealing. Figure S11a&b show the AFM images of SRO flakes across the edge of the flake (Fig.   S11a) and on the drum (Fig. S11b). The line scan over the edge of the flake shows a step height of 14.2 nm (inset of Fig. S11a). Compared to the XRD data shown in the main text, which suggests a thickness of 6.29 nm there is an overestimation of the thickness by a factor of more than 2. This could be a result of the PPC residues as can be seen in both topography scans of Fig. S11a and b and an overestimation of the van der Waals gap due to water and/or dirt as described by Shearer nm which is still an overestimate compared to the 6.29 nm we expect from the XRD data but is reduced from the data taken before annealing. Annealing can remove a large portion of the PPC residues. Also, a reduction in the amount of buckling is seen in Fig. S11d. Before annealing, the SRO membrane shows larger buckling amplitudes (Fig. S11b), likely arising from the PPC stamping process. However, after annealing the buckling height is largely reduced. S.X. EXPLODED DRUM Figure S12 shows atomic force microscopy (AFM) images of a SRO flake on cavities of SiO 2 /Si with pre-patterned electrodes. Shown device is annealed at 300 • C for 15 minutes. After annealing the device is bonded and loaded into a Oxford He flow cryostat. Just prior to loading, the membrane is in a flat configuration as shown in Fig. S12a. In the process of loading, the membrane bulges up due to the pressure difference between the cavity, which is filled with ∼1 bar air and the cryostat which is pumped to ∼1 mbar before letting the He to flow. After the attempt to measure the electron transport in the cryogenic temperatures we removed the sample and observed the drum using AFM. As shown in Fig. S12b, the drum had been torn off from the device. We hypothesize that this has occurred in a violent fashion as illustrated in Fig. S12c. During the pumping phase, the membrane may have "exploded" from the device due to a sudden change in the pressure. Having sealed, the pressure difference between the cavity and the sample space in the cryostat will have had ∆P ∼ 1 bar.

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FIG. S12. Atomic force microscopy (AFM) images of an annealed SRO flake a before loading into a vacuum chamber and b after loading into a vacuum chamber. c Illustration of the explosion process in annealed SRO drum. In ambient conditions, SRO flake is in the flat configuration. When the sample chamber is abruptly pumped, the membrane bulges up due to the pressure difference between the cavity and the sample chamber.
At base pressure of ∼10 −3 bar, the membrane bursts leaving a SRO flake with a hole in the center.

Method
Acoustic pulses in the GHz range are generated and detected using a picosecond ultrasonics technique 6 . By locally heating the sample with a 100 fs pump pulse, an acoustic pulse is generated. Using a probe pulse of the same duration, the acoustic reflections arriving back at the surface of the sample are measured. In this pump-probe experiment, the acoustic echoes are measured with the probe repetition rate at a slight offset from the 100 MHz pump, regulated by an asynchronous optical sampling (ASOPS) system from Menlo Systems. The pump and probe lasers are femtosecond erbium lasers (1560 nm), doubled in frequency (780 nm) for the probe. The average output power of the pump laser is ∼100 mW, and the one of the probe laser is set between 2 and 5 mW. Since the pump and probe repetition rates have a slight offset between them, at every next pulse the time of arrival between the pump and probe is slightly delayed in time. This way, the probe scans through the entire time window between 2 pump pulses (10 ns).
In the setup (Fig. S13), the probe beam is expanded to an appropriate size and passed through a half waveplate to achieve the correct polarization to be transmitted by the polarizing beam splitter.
A quarter waveplate then shifts the initial linear polarization to an elliptical polarization. After passing through a dichroic mirror, where the pump path joins the probe path, the beams are focused on the sample through a sapphire plate, used for ultrasonics detection by means of conoscopic interferometry 7 . On the sample, the pump beam is absorbed to generate the acoustic waves. A part of the probe beam containing the acoustic signal is reflected. Then the quarter waveplate ensures that the reflected path is reflected towards the photodetector by the polarizing beam splitter. In this path, an iris diaphragm cuts out a part of the light, which is necessary for the conoscopic interferometry. A 250 MHz bandwidth, silicon based, amplified photodetector is used in this setup, allowing to detect each individual pulse.
To acquire the data we use a 600 MHz lock-in amplifier from Zurich Instruments with the additional Boxcar option. This option allows to combine a Periodic Waveform Analyser (PWA) and a Boxcar. Using the boxcar, the energy contained inside each detected probe pulses is extracted. window this pulse can now be integrated and the amplitude can be derived (Boxcar). A second oscillator at the offset frequency between the pump and probe lasers, is also linked to the measurement. Using the phase of this second oscillator, the samples are divided in bins that are associated to corresponding time stamp within the measurement at which the sample was taken. By calculating the amplitude in each of this bins using the boxcar method and then concatenating them, the envelope signal of all the pulses is reconstructed.

Raw data
In the raw signal (Fig. S14), increases in the sample temperature caused by the pump laser pulses can be seen in the left and middle graph after a few ps. The effect is much higher in the non-annealed sample. This could be explained by the adhesion to the substrate. In the annealed sample, the improved adhesion facilitates a more efficient heat diffusion into the substrate, while in the non-annealed sample, it stays more confined inside the Au/Cr/SrTiO 3 assembly.
After ∼200 ps, a parasitic signal can be seen (also present without the pump excitation). This parasitic signal and the temperature increase are the origin of the high level component under ∼20 GHz in the spectra (Fig. S14 right). The part of the signal between the temperature increase and the parasitic signal (∼50 ps -200 ps) correspond to the acoustic signal, which is partially masked by the parasitic signal, as it can be seen in the non-annealed sample. The components of the spectra around ∼20 GHz and ∼57 GHz correspond to the frequency of these acoustic standing waves which are absent from the spectrum of the signal without excitation (Fig. S14 right, plotted in yellow) and are weaker in the annealed sample (Fig. S14 right, plotted in orange).

Filtered data
The signals are then high-pass filtered using a 18 GHz cut-off frequency to remove the parasitic background signals and the low frequency components of the temperature increase (Fig. S15).
The acoustic waves become much more visible, as well their associated components in the Fourier spectra.

Fitting a sinusoidal envelope
Only the part of the signal corresponding to the acoustic waves is then considered. This one is firstly smoothed using a moving average filter on 5 samples and is then fitted using a minimisation algorithm to find the parameters of a damped sine as the following (Eq. S.1): correspond to the filtered raw data of non-annealed and annealed samples respectively, the green to the smoothed signal and the dashed red lines to the fit using Eq. S.1.

Calculations of the results
The theoretical resonance frequencies are calculated from the expressions of standing waves in a medium, as given by Greener et al. 8 : for an unbounded medium (total debonding case, i.e. free surface at each boundary) and for a bounded medium (perfect adhesion case, i.e. loaded surface with continuity of stresses and displacement at the boundary with the substrate and free surface boundary condition at the other boundary of the structure). In the Eqs. S.2 and S.3, n is the order of the harmonic, c L eq = c L1 c L2 h eq c L1 h 2 +c L2 h 1 is the equivalent longitudinal wave velocity in the Au/Cr/SrTiO 3 assembly with c L1 and c L2 respectively the longitudinal velocity in the Au and SrTiO 3 layer. h eq = h 1 + h 2 is the total thickness of the assembly with h 1 = 30 nm the thickness of the Au layer and h 2 = 80 nm the one of the SrTiO 3 layer. The chromium layer is here neglected due to its small thickness (3 nm) with respect to the total thickness of the structure and with respect to the acoustic wavelength (of the order of 100 nm).
The reflection coefficient is then deduce from the following formula, also used by Greener et al. 8 : where |A p | is the absolute value of the amplitude after p reflections of the acoustic wave inside the structure, |A 0 | the initial amplitude of the wave, |R ac | the absolute value of the reflection coefficient in amplitude. From the reflection coefficient, it is possible to deduce the longitudinal interfacial stiffness K L , characterizing the adhesion between both materials at the interface 9 : where Z m = c Lm ρ m the acoustic impedance of the medium m with ρ m its density. Here, m = 2 for the SrTiO 3 and m = s for the substrate (SiO 2 ). For all these calculations, the values of c L1 , c L2 , c Ls , ρ 2 , ρ s have been taken from literature [10][11][12] and are given in Table S.XI Figure S17 shows the variations of the reflection coefficient in amplitude by varying the interfacial stiffness at the frequency f 1U = 21 GHz.

COMSOL simulations
The Finite Element Method simulations were performed using the heat transfer in solid and solid mechanics modules of the software COMSOL Multiphysics. The two modules were coupled together using the multiphysics thermal expansion module. The laser excitation was modeled as a heat source with similar characteristics than the pump laser pulses. The acoustic waves were detected using a point probe measuring the normal displacement at the surface of the 2D sample.
To simulate the total debonding, only an Au/SrTiO 3 sample was considered using free boundary condition at each end. To simulate a perfect adhesion case, an Au/SrTiO 3 /SiO 2 sample was  considered with a "perfect" interface (corresponding to a case where K L → ∞ in Eq. S.5 ).
A triangular meshing was used with a maximum element size of 2.5 nm in Au and 4 nm in SrTiO 3 to have minimum ∼15 elements per wavelength at 60 GHz in each materials. A coarser meshing (10 nm) was used in the SiO 2 substrate since the propagation of the waves in this material is not really of interest here. Its thickness has been chosen large enough to not have any backward 27 reflection coming from the bottom of the substrate. A time dependent study is then processed with a time step of 0.2 ps to get more than 60 samples per period of the acoustic waves at 60 GHz.
The results of the simulations are shown in Fig. S18. For the case with the substrate (corresponding to a perfect adhesion, orange curve on the Fig. S18), the reflection coefficient in amplitude |R ac | of 0.45 is found: this case corresponds to the limit K L → ∞, as shown in the Fig.   S17. The case without the substrate (corresponding to a total debonding, blue curve in the Fig.   S18), the reflection coefficient is equal to 1: this case corresponds to the limit K L → 0, as shown in Fig. S17.