Graphene-based capacitive monolithic microphone with optimized air gap thickness and damping Open Access

A microphone is a transducer that converts sound signals into electrical signals.^1,2 As sound is an important information carrier in our daily life, there has been extensive studies about microphones. Many sound sensing mechanisms have been studied and applied to the fabrication of microphones. For example, there are optical,^3,4 piezoelectric,^5,6 piezoresistive,^7,8 and capacitive microphones. Capacitive sensing is a common mechanism in microelectromechanical systems (MEMS), widely applied to accelerometers,^9,10 pressure sensors,^11,12 and other devices.^13–15 A capacitive microphone^16–18 detects the capacitance change due to sound pressure. A fixed plate, a movable plate, and the air gap between them form the capacitance-change-sensing structure. The movable plate vibrates in response to sound pressure; thus, the variance in capacitance converts sound signals to electrical signals.¹⁷ 

Since the successful synthesis of graphene in 2004,¹⁹ its application in MEMS acoustic sensing devices^2,20–22 has attracted much attention. Graphene is a two-dimensional (2D) material, which consists of only one or a few layers of carbon (C) atoms. The ultralow thickness of graphene not only agrees with the trend of miniaturization in the MEMS field, but also promises high sensitivity in devices with graphene-based vibrating structures.^23–25 In addition, graphene has many other outstanding mechanical, electrical, and thermal properties. Mechanically, graphene is a strong and light material with high intrinsic strength (∼130 GPa),²⁶ high Young's modulus (up to 1 TPa),^26,27 and relatively low mass density (2200 kg/m³).²⁸ Electrically, high electron mobility (2 00 000 cm² V⁻¹ s⁻¹)²⁹ makes graphene an ideal material for electrical connections. Thermally, graphene's superior thermal conductivity (∼2000–5300 W/mK)^30,31 and a unique negative coefficient of thermal expansion (CTE) (∼−7 × 10⁻⁶ K⁻¹)^30,32 bring the possibility of electrothermally actuating graphene-based bilayer membranes, as electrothermal actuation of a bilayer system relies on the difference in the CTE of different materials.^23,33–37

In previous research, synthesizing,³⁸ transferring,^39,40 and suspending^23,41 large graphene membranes have been accomplished, demonstrating the possibility of fabricating MEMS capacitive microphones with a graphene-based membrane as the movable plate. Research has found that the drum structure where a membrane is clamped along the periphery has a higher quality factor compared to doubly clamped (bridge) structures, and the quality factor also increases with the increase of the resonator size.⁴² A higher quality factor indicates lower energy dissipation. Previously, our team have fabricated drum-structure (also called open-cavity structure) resonators.^23,41 Figure 1(a) shows the graphene-based membranes that have been clamped on silicon dioxide (SiO₂) with 3.5-mm diameter cavities.^23,41 Poly(methylmethacrylate) (PMMA) has been attached to graphene for mechanical support, forming a bilayer membrane. There was not a fixed plate (also called a back plate) so that the capacitive-sensing structure was not formed and the thickness of the air gap is infinite.

When the fixed plate is added to the structure, placed below the suspended membrane, a closed-cavity structure is formed; see Fig. 1(b).⁴³ However, in a closed-cavity structure, air is trapped inside the closed cavity so that the effect of viscous damping cannot be neglected. When the lateral dimension is kept the same (3.5 mm diameter), smaller air gap thickness results in larger damping.⁴⁴ Damping causes the decrease of the vibration amplitude, influencing the sensitivity of microphone. When there is too large damping, the membrane stops vibrating. Interestingly, damping is not the only way that the air gap thickness influences the sensitivity. The air gap thickness also influences the static capacitance of the microphone, thus influencing the sensitivity. In an ideal environment without damping, smaller air gap thickness results in larger sensitivity.⁴⁵ To optimize the sensitivity, trade-off between static capacitance and damping is a necessary consideration for designing the air gap thickness in a device with a closed-cavity structure.

In order to minimize the air gap thickness for better sensitivity, methods have been taken and two more structures have been designed to optimize the damping. One method is to fabricate the top and bottom plates on two separated chips and assemble them manually, adhering with silver paste; see Fig. 1(c).⁴⁶ Thus, air leakage between two chips helps to decrease the damping so that the air gap could be decreased to ∼8 μm. However, integration has always been the trend in the MEMS field, and the manual assembly makes the process more complex and uncontrollable. Figure 1(d) shows the other method, which is to etch through the back plate and introduce vent holes,⁴⁵ like many other microphones did.^47–49 However, vent holes introduce acoustic noise.⁵⁰ In addition, too many holes will reduce the backplate area, increasing the backplate compliance while reducing capacitance.⁵¹ It is necessary to know whether both the thickness of the air gap and the number of vent holes could be reduced while optimizing the damping so that the membrane could vibrate.

In this work, we present a graphene-based capacitive monolithic microphone with a 2 μm air gap and only one vent hole, demonstrating the possibility to minimize both the thickness of the air gap and the number of vent holes. The design, fabrication, and characterization are introduced. The suspension of a graphene-based membrane has been confirmed with Coherence Scanning Interferometry (CSI). During the fabrication process, a combined wet and dry etching of silicon dioxide (SiO₂) has been used, which effectively prevents hydrogen fluoride (HF) from attacking the aluminum (Al) electrodes. The vibration of the membrane when actuated electrostatically and electrothermally has been observed with a Laser Doppler Vibrometer (LDV). The microphone's response to sound has been measured by both LDV and a read-out circuit.

Figure 2 shows the design of the capacitive microphone. The whole device sits on a 7 × 7 mm² chip, which has been diced out of a 3-in. silicon (Si) wafer. From the side view [Fig. 2(a)], the top plate, the back plate, and the cavity can be seen. Figure 2(b) shows the top view of the device.

Figure 2(c) illustrates a rotated view of the top plate, which consists of a bilayer membrane and top electrodes. The bilayer membrane is the vibrating part that responds to sound, which is ∼350 nm PMMA on ∼2 nm (6 layers) graphene. The top electrodes made of 500-nm thick Al are wire-bonded, providing electrical connections. The PMMA/graphene membrane has been transferred to the top electrodes.

The back plate consists of the Si substrate, a 70 nm layer of thermal SiO₂, and the bottom electrodes. The bottom electrodes are also made of 500-nm thick Al, the same as the top electrodes. The Si substrate has been etched through to create the 100-μm diameter circular vent hole.

The top plate and the back plate are separated by a 2-μm dielectric layer of SiO₂, which determines the thickness of the air gap to be 2 μm. To connect to the bottom electrodes, the SiO₂ has been etched through to form vias, and the vias have been filled with Al. The 3.5-mm diameter cavity has been created by etching through the SiO₂, on which the bilayer membrane will be suspended.

A 75 mm Si wafer with the thickness of 380 ± 10 μm has been used for fabricating the graphene-based capacitive monolithic microphone. Figure 3 shows the schematic of a fabrication process. First, 70 nm SiO₂ has been deposited on both sides of the wafer by low-pressure chemical vapor deposition (LPCVD), where the front side SiO₂ could separate the substrate and the bottom plate [Fig. 3(a)]. On top of the front side thin oxide, 500 nm Al has been sputtered and patterned by lift-off as the bottom electrode [Fig. 3(b)]. Next, another 2 μm oxide has been deposited by plasma-enhanced chemical vapor deposition (PECVD), burying the bottom electrode underneath [Fig. 3(c)].

In order to create the 3.5-mm diameter cavity and vias for connecting to the bottom electrodes, the oxide layer needs to be etched through to expose the Al. There are two common methods of etching SiO₂, including a wet method with buffered hydrogen fluoride (BHF or a buffered oxide etch, BOE) and a dry method by reactive ion etching (RIE). However, both methods have drawbacks. In this work, the Al electrodes underneath will be attacked by BHF if using the wet method. Meanwhile, the dry method is not suitable for etching SiO₂ as thick as 2 μm, because long-time RIE not only leaves residues on Al surface, which are hard to remove, but also results in the difference in the etch rate at different locations even on the same wafer, leading to difficulty in quality control. To eliminate the drawbacks of the two methods, a combined wet and dry method has been applied to the SiO₂ etching steps of this work. First, the wafer has been wet etched with BHF for a short time and taken out of the solution, rinsed, and dried before exposing the bottom Al layer. The subsequent etching is completed by the dry method. The wafer with remaining SiO₂ is put into the JLS RIE80 etcher, etched with CF₄ and O₂ plasma by RIE, and taken out regularly to measure the thickness of the remaining SiO₂ (by optical reflectometry with a Nanospec AFT 180&3000). The combined wet and dry etching method prevents Al from being attacked and shortens the time for dry etching. After several tests, 3.5 min wet etching and 41 min dry etching have been found to produce relatively good etching quality for 2-μm-thick SiO₂, which has been applied to the following two SiO₂ etching steps.

As Fig. 3(d) shows, the vias have been patterned photolithographically and etched by the combined wet and dry method first. In this step, the ∼70 nm back side SiO₂ has been removed. After that, another layer of 500 nm Al has been deposited by lift-off to the front side, filling in the vias and forming the top layer electrodes and pads [Fig. 3(e)]. Next, the combined wet and dry etching method has been used again for etching out the 3.5 mm wide cavity [Fig. 3(f)]. Then, from the backside of the wafer, the 100 μm vent hole has been patterned photolithographically and the bulk Si has been etched through by deep reactive ion etching (DRIE) [Fig. 3(g)]. At this point, the 3-in. wafer has been diced into 7 × 7 mm² chips, each containing a single device. Finally, a piece of a PMMA/graphene membrane is wet transferred to the chip, dried, and baked [Fig. 3(h)]. The wet transfer of PMMA/graphene has been reported elsewhere.^23,41

Figure 4 shows the optical microscope image of a fabricated device, which has been taken with a Leica microscope. As both the membrane and SiO₂ are transparent, bottom electrodes under SiO₂ can be observed in the image. For electrical connections, the chip has been glued into a 2 × 14-pin package, and the electrodes have been wire-bonded.

Suspension of a membrane has been confirmed by Coherence Scanning Interferometry (CSI) with a Polytec TMS-2400 TopMap Micro.View+. The light source used was at a wavelength of 525 nm.

Characterization of the device performance has been achieved via two alternative actuation mechanisms: electrostatic actuation and electrothermal actuation. For electrostatic actuation, direct current (DC) voltage and alternating current (AC) voltage have been applied between the top (G) and bottom (A) electrodes so that an electrostatic force drives the membrane to vibrate.⁵² For electrothermal actuation, DC and AC voltages have been applied between two top (G) electrodes, generating electric current in the membrane, which produces Joule heat, so that the membrane expands thermally. Due to different CTEs of graphene and PMMA, the thermal expansions in the two layers differ, creating the strain that drives the membrane to vibrate.^23,41 The response of the membrane has been measured with a Polytec MSA-400 laser Doppler Vibrometer (LDV), which focuses a narrow point of laser light onto the membrane and records the vibration amplitude by measuring the Doppler shift with respect to the incident signal.⁵³ In this work, the laser point has been focused on the membrane above the center of the vent hole, except for measuring the mode shapes, because the largest amplitude is observed at the membrane above the center of the vent hole. The reason could be that the damping is smallest at the area of the vent hole. The input signal has a frequency sweep from 100 Hz to 200 kHz with a sampling frequency of 1.28 MHz and a resolution of 39.0625 Hz. Velocity data have been collected and transformed into displacement data, with a fast Fourier transform (FFT) analysis. An average of three scans has been used to minimize the noise in the measured velocity data.

In addition to the electrostatic and electrothermal actuation mechanisms, it is important to test the device under more realistic acoustic actuation, from a nearby sound source (in this case, a loudspeaker). As Fig. 5 shows, the fabricated microphone has been connected to a read-out circuit.⁴⁶ The displacement of a membrane and its output voltage $( V O U T)$ in response to the acoustic actuation has been measured. For measuring the sound pressure, a calibrated measurement microphone (GRAS 46 BE 1/4″ CCP Free-field Standard Microphone) has been placed as close as possible to the diaphragm of the fabricated microphone and connected to a computer in order to record a reference acoustic signal, which can then be translated into units of acoustic Pascals (Pa). Audio was produced and recorded on the computer using Audacity(R) (version 3.5.1)⁵⁴ and Reaper (version 7.16)⁵⁵ software. The recordings of the reference microphone have been processed by MATLAB to find the root-mean-square (RMS) pressure of the sound signal. As Fig. 5 shows, $C M$ is the electrical capacitance of the microphone fabricated in this work. The two plates of the capacitive microphone have been connected to a DC bias voltage of 1 V $( V C)$ and the gate of a metal-oxide-semiconductor field-effect transistor (MOSFET), respectively. The base and source of the MOSFET have been grounded, and the drain has been connected to a passive band-pass filter to remove unwanted low- and high-frequency noise. The lower and upper cut-off frequencies of the filter are 159 Hz and 16.8 kHz, respectively. Therefore, only output signals in the frequency range of 200 Hz–16 kHz were recorded. The drain of the MOSFET was also connected to a drain resistor (R_D = 390 Ω) and V_DD = 13.1 V. A ×50 amplifier has been connected before read-out of the voltage signal $V OUT$⁠. More details of the read-out circuit can be found elsewhere.⁴⁶ 

A 0.8 × 0.7 mm² area membrane above the 100-μm vent hole has been scanned by CSI, and Fig. 6 shows the result. Figures 6(a) and 6(b) show the 2D and 3D image of the surface topography in the same area, respectively. The static deformation of a scanned membrane is ∼0.8 μm so that the aspect ratio of scanned membrane length over deformation is ∼1250. From Figs. 6(a) and 6(b), a small defect could be seen, which we hypothesize may be explained by the nonuniform distribution of spin-coated PMMA, but the membrane is not collapsing or touching the bottom structures.

Figures 7 and 8 depict the frequency responses of an electrostatically and electrothermally actuated membrane, respectively. A single resonance peak has been observed between 0 and 200 kHz. It is worth pointing out that there is no resonance peak within the frequency range of a human auditory system (about 20 Hz–20 kHz)⁵⁶ so that the microphone's response to audio sound will be relatively flat.

Different sets of AC and DC voltages have been applied for actuation. For electrostatic actuation, the DC voltage has been kept constant at 4 V while the AC voltage increased from 0.5 to 4.5 V in a 0.5 V increment, and the results are shown in Fig. 7(a); afterward, the AC voltage has been kept constant at 4.5 V while the DC voltage increases from 0.5 to 4.0 V in a 0.5 V increment, and the results are shown in Fig. 7(b). For electrothermal actuation, the DC voltage has been kept constant at 1 V while the AC voltage has been sweeping from 2 to 9 V in a 1 V increment, and the results are shown in Fig. 8.

For both actuation methods, the resonance peaks have been observed to have a wide shape, which indicates small quality (Q) factors and large energy dissipation. We hypothesize that the reason could be the large air damping due to the small air gap between two plates. Comparing the two actuation methods, it can be found that electrothermally actuated membranes have a smaller displacement amplitude and a larger resonant frequency compared to an electrostatically actuated membrane. In addition, AC and DC voltages have an influence on the resonant frequency and the displacement amplitude, which will be discussed in Secs. III B 1 and III B 2.

Figure 9 shows the mode shapes of the membrane at a resonant frequency. For both electrostatic and electrothermal actuations, (0, 1) modes have been observed at the part of membrane over the vent hole; see Figs. 9(a) and 9(b), respectively. Interestingly, our previous work observed a membrane on an open cavity to vibrate at the (0, 1) mode.²³ The mode shape of the membrane over the vent hole in this work is similar to the membrane over an open cavity in the previous work. The reason could be that the air gap thickness at the vent-hole part is infinite, similar to an open-cavity structure.

Because of the similar fabrication process and the actuation voltage, we assume a similar tension $N i+ N t$ as previous works. The parameters for calculation can be found in Table I. If using the radius of the vent hole, 50 μm, in the calculation, the resonant frequency should be around 114.1 kHz, close to the actual ∼112.18 kHz. The calculation result shows that the resonant frequency is determined by the size of the vent hole, which implies that the model for the part of the membrane over the vent hole is very similar to an open-cavity structure model.

In addition to the small part of the membrane over the vent hole, the mode shape of the entire suspended membrane has been measured. Compared to electrothermal actuation, electrostatic actuation results in a larger displacement amplitude, which makes the vibration clearer and easier to observe. Therefore, electrostatic actuation was chosen to measure the vibration of the entire suspended membrane. Figure 9(c) depicts the vibration of the entire suspended membrane under electrostatic actuation at a resonant frequency.

From Fig. 9(c), it can be seen that the entire suspended membrane has been vibrating, but different parts vibrate at different amplitudes. The largest amplitude of displacement has been observed to be at the part of the membrane over the vent hole, because the damping is smallest at the area of the vent hole. The second largest amplitude of displacement has been observed at the parts of the membrane over the bottom electrodes. The inset of Fig. 9(c) shows the design of bottom electrodes. An explanation for the second largest amplitude could be that the electrostatic force from the bottom electrodes has the largest effect on parts of the membrane that is right above the electrodes. However, compared to the displacement of the membrane over the vent hole, the displacement of the membrane over bottom electrodes is too small to be measured because of the large damping. The curve in Fig. 9(c) plots the difference between displacement of the membrane above the center of the open cavity and vibration of the membrane above the center of bottom electrodes.

As Figs. 7 and 8 show, for both electrostatic and electrothermal actuations, larger actuation voltage results in larger displacement. Figure 10 illustrates the effect of actuation voltages on the displacement amplitude at a resonant frequency.

In the case of electrostatic actuations, Figs. 10(a) and 10(b) show a linear relationship between the displacement amplitude and the AC/DC voltage, which corresponds to the theory of electrostatic actuation that the vibration has been introduced by an electrostatic force, which is proportional to AC and DC voltages.⁵² The displacement amplitude increased from 3.38 to 25.62 nm with the AC voltage of 0.5–4.5 V and from 7.56 to 25.62 nm with the DC voltage of 0.5–4.0 V.

When it comes to electrothermal actuation, the actuation voltage generates a temperature gradient between the bilayer membrane because of the difference in the material's CTE. The temperature gradient introduces thermal stress to drive the membrane into resonance. As the displacement amplitude is proportional to the thermal stress, a linear relationship between the displacement amplitude and the square of the AC voltage could be derived. Figure 10(c) demonstrates the quadratic relationship between the displacement amplitude and the AC voltage.^23,57,58 Our team have previously completed finite element analysis (FEA) simulation to confirm the relationship between thermal stress and input voltages.⁴¹ With the increase of the AC voltage from 2 to 9 V, the displacement amplitude increased from 0.70 to 1.58 nm.

In addition to the change in the displacement amplitude, the resonant frequency has been observed to shift when varying the actuation voltage. Figure 11 shows the effect of AC and DC voltages on resonant frequencies. In the case of electrostatic actuation, when increasing the AC/DC voltage, the resonant frequency shifts upward (4.27% for AC 0.5–4.5 V and 5.13% for DC 0.5–4 V) because the increase of the actuation voltage induces spring hardening effects.⁵⁹ 

However, interestingly, the trend is opposite for electrothermal actuation; i.e., the resonant frequency shifts downward (6.43% for AC 2–9 V) with the increase of the AC actuation voltage. The downward frequency shift of an electrothermally actuated membrane probably results from the reduction of thermally induced membrane tension.⁴¹ The possibility of tuning the resonant frequency by varying the actuation AC/DC voltage enables the device to be applied to a wider frequency range, which might be useful for future applications.

Figures 12(a) and 12(b) plot the mechanical and electrical sensitivity against sound frequency (200 Hz–16 kHz), respectively. It can be observed from the plots that both mechanical and electrical sensitivity increases slightly with frequency, which agrees with the displacement-frequency curve in Figs. 7 and 8 that in electrostatic and electrothermal actuations, displacement increases with the frequency between 200 Hz and 16 kHz. The mechanical sensitivity of the membrane is in the range of 5.81–491.23 pm/Pa. Also, the electrical sensitivity is in the range of 0.0003–2.21 mV/Pa, which is also −131.20 to −53.12 dBV relative to 1 V/Pa.

The mechanical sensitivity shows the capability of the membrane in converting a sound signal to a mechanical signal, and the electrical sensitivity shows the capability of the microphone and the read-out circuit in converting a sound signal to an electrical signal. In this work, the average mechanical sensitivity is 117.90 pm/Pa, and the average electrical sensitivity of a microphone is 0.23 mV/Pa (−72.74 dBV relative to 1 V/Pa). Table II shows the comparison of this work to some previous MEMS microphones, including a microphone with a silicon membrane, a microphone with a polysilicon membrane, two microphones with graphene or PMMA/graphene membranes, and our previous works with PMMA/graphene membranes. The microphones with higher sensitivities come with better ventilation, i.e., a two-chip assembled structure, a larger air gap, or more vent holes. Compared to the previous work, the microphone fabricated in this work may not be more sensitive, but its ability in sound sensing demonstrates the possibility to minimize the air gap thickness in graphene-based microphones while reducing the number of vent holes.

In summary, we have designed, fabricated, and characterized a graphene-based monolithic capacitive microphone. The microphone has an air gap as thin as 2 μm, and the damping has been minimized with a single vent hole (100-μm diameter circular) in the back plate. The bilayer membrane of ∼350 nm PMMA and ∼2 nm (∼6 layers) graphene has been observed to be suspended above the cavity. A method to etch SiO₂ has been optimized for better quality control.

The membrane has been driven into resonance electrostatically and electrothermally at different actuation voltages. The actuation voltage influences the displacement amplitude and the resonant frequency for both actuation methods. The increase of the actuation voltage results in the increase of the displacement amplitude for both actuation methods. With the increase of the actuation voltage, the resonant frequency has been observed to shift upward for electrostatic actuation and downward for electrothermal actuation. The frequency tunability by up to 6.43% reveals the promising possibility in operation in a wider frequency range for future works. In the audio test, the average mechanical sensitivity has been measured to be 117.90 pm/Pa and the average electrical sensitivity to be 0.23 mV/Pa (−72.74 dBV relative to 1 V/Pa).

The microphone's performance demonstrates the possibility to minimize both the thickness of the air gap into 2 μm and the number of vent holes into one, though at relatively lower sensitivity. In future work, the number of holes could be increased slightly to optimize the sensitivity, but too many vent holes should be avoided because they may influence the capacitance and backplate compliance severely. At the same time, study of the noise could be an important topic.

We acknowledge help from Polytec via use of the tool TMS-2400 TopMap Micro. View+. This work has been performed in the cleanroom in the Scottish Microelectronics Centre (SMC) and in the acoustics lab of the Acoustics & Audio Group, University of Edinburgh. The authors acknowledge the financial support of the UK Engineeirng and Physical Science Research Council (EPSRC) for our work.

The authors have no conflicts to disclose.

Yun Jiang: Data curation (lead); Formal analysis (lead); Visualization (lead); Writing – original draft (lead). Graham S. Wood: Methodology (equal); Writing – review & editing (supporting). Michael J. Newton: Resources (equal); Software (equal); Supervision (supporting); Writing – review & editing (supporting). Peter Lomax: Resources (equal); Supervision (supporting); Writing – review & editing (supporting). Rebecca Cheung: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.