Capacitive pressure sensing with suspended graphene – polymer heterostructure membranes †

We describe the fabrication and characterisation of a capacitive pressure sensor formed by an ultra-thin graphene–polymer heterostructure membrane spanning a large array of micro-cavities each up to 30 μm in diameter with 100% yield. Sensors covering an area of just 1 mm show reproducible pressure transduction under static and dynamic loading up to pressures of 250 kPa. The measured capacitance change in response to pressure is in good agreement with calculations. Further, we demonstrate high-sensitivity pressure sensors by applying a novel strained membrane transfer and optimising the sensor architecture. This method enables suspended structures with less than 50 nm of air dielectric gap, giving a pressure sensitivity of 123 aF Pa mm over a pressure range of 0 to 100 kPa.

solutions surface (Figure 1, step 2b).Similarly to step 1, the tape supported membrane is cleaned in 3 subsequent DI water baths before it is removed from the final bath with tweezers using the tape as a handle (Figure 1, step 2c).The next step is to form the target substrate comprising cavities and electrodes (Figure 1, step 3).On a separate Si/SiO 2 substrate, a positive photoresist mask (Shipley S1813) is exposed using an optical lithography system (Microtech LaserWriter).The substrate is then developed (Shipley MF319) and patterned by deep reactive ion etching using CHF 3 and Ar gas (Oxford Plasma Lab 100) to form an array of circular or hexagonal holes of a given diameter, periodicity and depth, arranged in various patterns such as a hexagonally packed lattice (Figure 1, step 2b).The remaining photoresist is then removed with acetone and another positive photomask is formed using a double layer resist (Shipley PMGI and S1813) to define electrode structures.A thermal evaporator (Moorfield Nanotechnology) is then used to deposit 5 nm chromium followed by 70 nm gold followed by removal of the double layer photoresist using developer (MF319) and acetone (Figure 1, step 3c).In the final step the tape supported graphene-PMMA film is aligned with the target substrate using an in-house built transfer system (Figure 1, step 4a). 1 The graphene-PMMA film is then brought into contact with the substrate and the edges of the film are torn using a sharp tipped tool, releasing the tape window support (Figure 1, step 4b).In order to optimise the fabrication procedure we employed a series of optical and mechanical techniques that can be used in parallel to identify the failure mechanism of collapsed membranes.Sensors were first imaged by optical microscopy (OM) to check for rips, cracks or contaminants in the graphene-polymer film (Figure 2a, arrow i).Samples with full covera ge and homogenous film transfer were then analysed by Raman spectroscopy and atomic force microscopy (AFM).Renishaw Streamline TM Raman mapping allowed us to map the signiture G (1580 cm -1 ) and 2D (2680 cm -1 ) peak intensities over the entire sample area.We found that the G peak intensity gave the highest contrast between suspended and substrate-supported regions due to laser interference effects from the variation in effective refractive index through air in comparison to SiO 2 (Figure 2a, RM).We note that great care must be taken when identifying suspended membranes since contaminants can show an enhanced Raman signal that is easily mistaken for a suspended membrane (arrow i).Further characterisations of successfully transferred films is undertaken by AFM Quantitative Nanomechanical Mapping (QNM). 2 This mode of AFM allows us to create high resolution maps of the height (AFM-height) and effective elastic modulus (AFM-modulus) of our device.The combination of height and modulus data allows us to cross-check if membranes are truly suspended and highlights any cracks or tears (Figure 2a, arrow iii) in the membranes that may not be visible from optical microscopy and Raman mapping.For comparison, an optimised graphene-polymer transfer (Figure 2b) shows a homogenous array of suspended graphene-polymer membranes.The AFM height scan in th right imag of Figure 2b shows that the array of mmbranes consists of evenly suspended membranes that gently sag into the cavities.

Supplementary Discussion 3: Characterisation of gas permeability of graphene-polymer membranes
In order to characterise the gas permeability of the graphene-polymer membranes we applied a micro-blister inflation technique.Firstly, pressure sensor samples were inserted into a pressure chamber equipped with a commercial reference pressure sensor and a gate valve, allowing precise control over the chamber pressure.
The chamber was pumped with N 2 gas to 400 kPa and left for 24 hours allowing gas to diffuse into the microcavities, equilibrating the pressure across the membrane.Samples were then removed from the pressure chamber, causing the membrane to form a blister above the micro-cavity.Samples were then mounted on an AFM within 5 minutes of removing samples from the pressure chamber.We then monitored the maximum point of deflection, of the micro-blisters periodically over 3 hours.Figure 3a shows an optical micrograph of , a device under test at equilibrium pressure and the AFM height map and cross-section in Figure 3b and c shows the same device immediately after sample removal from the pressure chamber.Figure 2d  This suggests that the reference pressure reading used to conduct pressure sensing measurements would have limited accuracy as the cavities leak gas over time.We repeated this deflation experiment for 8 bare graphene and 285 nm graphene-polymer samples each for comparison and the membrane deflection is plotted over time in Figure 3d.The deflation of bare graphene samples is negligible as expected due to its gas impermeability and ultra-strong adhesion to the micro-cavity edge, providing a gas tight seal. 3,4The slight decrease in deflection is likely due the porosity of the SiO 2 as previous reports suggest.285 nm graphenepolymer membranes on the other hand show a rapid decrease in deflection.We attribute this increase in gas leakage due to the increased bending rigidity of thicker membranes, reducing the ability of membranes to fully conform to the substrate and adhere via van der Waals forces.In addition, the use of a large scale transferred film, comprising a continuous CVD graphene sheet ensures minimal gas leakage through the membranes.
Instead, we expect the gas pressure in neighbouring micro-cavities to equilibrate via nano-channels along the substrate-membrane interface.To support this hypothesis we fabricated three substrates comprising arrays of cavities of varying density described by the ratio of micro-cavity diameter, to its spacing from neighbouring , cavities, .Figure 3e shows the distribution of times taken for 3 samples of varying cavity density with a  thickness of 140 nm to deflate to .This demonstrates the correlation between the leakage rate and / 0 = 0.5 micro-cavity density, suggesting that high density arrays are mostly limited to dynamic pressure sensing.
Moreover, it gives an indication of the timescales over which the measured sensor performance is representative of the model described above.We note that thermal treatment of the polymer-layer temporarily softens the graphene-polymer membrane allowing it to form an improved substrate-graphene interface that can further increase the gas impermeability of the membranes. 5

Supplementary Discussion 4: Pressure sensor calibration
We characterised the effect of surface adsorbates measuring the change in capacitance of a reference device using compressed air and nitrogen gas individually.The reference device comprised a 1 mm 2 graphenepolymer square transferred onto a plain Si/SiO 2 substrate with no cavities.The response of three consecutive pressure cycles between 0 and 200 kPa of the reference device is shown Figure 4a.Whilst compressed air gave a capacitance variation of approximately 0.1 pF over a 200 kPa pressure change, nitrogen gas showed negligible variations.Thus we conducted all pressure cycling experiments in a nitrogen atmosphere.We further investigated the onset of drift in devices by monitoring the capacitance of a cavity-baring device over an extended period of time when cycled between 0 kPa and 100 kPa in comparison to when kept at equilibrium pressure.Figure 4b shows that negligible drift is observed under static loading whilst cycling not only causes gradual decrease in drift during cycling, but also the sensitivity of the sensor before stabilising after some time.We attribute this behaviour to the initial relaxation of fabrication induced stresses which are readily relieved on multiple pressure cycles of the membranes.In order to ensure minimal drift and reproducibility in the sensor performance we cycled all sensors for several minutes before measurement.graphene-polymer membrane latches to the sub-cavity base at a and is realised again at a   = 5.9  , however, further experiments are required to confirm this. Figure 7c shows the dielectric loss   =-5.2  of both device designs as a function of applied gate bias from 0 V to 10 V. Whilst design 1 shows a relatively low loss of 0.016 at 0 V and minimal increase in loss at increasing gate bias, design 2 shows sharp spikes in loss throughout the positive voltage sweep.This further supports the charge leakage mechanisms described above.

+Figure 2 |
Figure 2 | Characterisation of graphene-polymer capacitive pressure sensor.(a) Optical micrograph (OM), Raman Map (RM), Atomic Force Microscope height map (AFM-height) and AFM modulus maps (AFM-modulus) of the same area of a graphene-polymer membrane sample in demonstrating the typical device artefacts encountered in the development; i: Contaminants that appear as suspended membranes, ii: Sagging membranes that appear as collapsed in AFM height maps, iii: Fractured membranes that appear as intact in AFM height maps.(b) Optical micrograph and AFM cross-section of optimised graphene-polymer array for comparison.Scale bars = 30 µm for all figures.

Figure 3|
Figure 3| Nitrogen gas leakage from graphene-polymer micro-blisters (a) An optical micrograph of a close packed array of 15 µm diameter membranes with a thickness of 140 nm at equilibrium pressure.Scale bar: 20 µm.(b) An AFM height map of the magnified area in Figure 2a pumped to 400 kPa resulting in micro-blisters.Scale bar 20 µm.(c) A cross-section of the white dotted line in Figure 2b shows the deflection of four micro-blisters inflated to 400 kPa.(d) The deflation of microblisters from 400 kPa over 157 minutes.Eight samples of each bare graphene, 140 nm and 285 nm graphene-polymer are displayed.Best fit lines of the bare graphene and 285 nm graphene-polymer samples are shown for clarity.(e) The time

Figure 4
Figure 4 |Calibration of pressure sensing system.(a) Variation of capacitance as a function of pressure of reference devices containing no cavities using compressed air and nitrogen pressurising gases of three consecutive pressure cycles between 0 and 200 kPa.(b) The change in capacitance of a single device when the pressure is cycled between 0 and 100 kPa compared to when the device is kept static.

Figure 7 |
Figure 7 | Sensor characterisation of second generation device.(a) A probe is contacted to the graphene-polymer membrane via a silver epoxy contact at the edge of the transferred film.Scale bar 100 µm.(b) Variation of capacitance over time of a second generation device (black) in reference to the sample chamber pressure.