A broadband, capacitive, surface-micromachined, omnidirectional microphone with more than 200 kHz bandwidth Michael L. Kuntzman and Neal A. Halla) Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78712
(Received 5 November 2013; revised 5 February 2014; accepted 14 April 2014) A surface micromachined microphone is presented with 230 kHz bandwidth. The structure uses a 2.25 lm thick, 315 lm radius polysilicon diaphragm suspended above an 11 lm gap to form a variable parallel-plate capacitance. The back cavity of the microphone consists of the 11 lm thick air volume immediately behind the moving diaphragm and also an extended lateral cavity with a radius of 504 lm. The dynamic frequency response of the sensor in response to electrostatic signals is presented using laser Doppler vibrometry and indicates a system compliance of 0.4 nm/Pa in the flat-band of the response. The sensor is configured for acoustic signal detection using a charge amplifier, and pffiffiffiffiffiffisignal-to-noise ratio measurements and simulations are presented. A resolution of 0.80 mPa= Hz (32 dB sound pressure level in a 1 Hz bin) is achieved in the flat-band portion of the response extending from 10 kHz to 230 kHz. The proposed sensor design is motivated by defense and intelligence gathering applications that require broadband, airborne signal detection. C 2014 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4874620] V PACS number(s): 43.38.Bs, 43.38.Gy, 43.38.Kb, 43.38.Lc [MS]
I. INTRODUCTION
Microphones with bandwidth extending beyond the audio range and up to hundreds of kHz and beyond have applications in several fields. In aeroacoustics, measurements with broadband microphone arrays and dynamic pressure sensors are used to study sources of noise of various aircraft components and to study turbulent boundary layers. Acoustic cameras utilizing nearfield holography techniques have been developed to study noise sources in many industrial noise control applications including automotive and manufacturing sectors. Broadband microphones are also used in biological studies. In recent studies, microphones were mounted atop bats to measure echolocation pulse intensity.1 The measurement range of interest in this study was 20–192 kHz. Broadband acoustic sensors are also applied in military and defense applications; including use in acoustic fingerprinting applications and sniper detection systems where muzzle blasts with spectral content up to 1 MHz is measured.2 Technologies used to address broadband microphone design include piezoresistive,3,4 piezoelectric,5,6 optical,7,8 and capacitive readout.9–11 Martin et al.9 summarizes and compares several recent works in this field. Because each application has unique requirements, not one technology fits all applications. Partial motivation for the present work is to develop an omnidirectional microphone that is compatible with a previously developed pressure gradient sensor,12 so that the sensors can be fabricated together on a single silicon die using the same surface-micromachining fabrication process to realize a miniature, broadband sensor array for acoustic localization applications.
a)
Author to whom correspondence should be addressed. Electronic mail: [email protected]
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This work presents an overview of the construction of the sensor, followed by presentation of a dynamic device model and verification using electrostatic actuation and laser Doppler vibrometry (LDV) measurements of the microphone diaphragm. Acoustic measurements are then presented along with signal-to-noise ratio (SNR) characterization. Generally speaking, in comparison to conventional instrumentation microphones, the purely surface micromachined acoustic sensor introduced may have advantages of small size and lower cost fabrication due to the simple surface-micromachined construction. The sensor uses materials stable to relatively high temperatures compared to lead zirconate titanate (PZT) and other Curietemperature limited ceramic based microphones, which may offer an advantage for some applications. The sensor fabrication could also easily be adapted to fabrication using silicon carbide, diamond, or other materials well suited for high-temperature and harsh environment applications. Compared to bulk-micromachined capacitive broadband microphones,9,13 the sensor introduced here has perhaps simpler fabrication but the disadvantage of smaller capacitance and higher noise. II. DESCRIPTION OF SENSOR
A scanning electron micrograph (SEM) of a fabricated prototype is presented in Fig. 1(a), and 3D CAD sections in Figs. 1(b) and 1(c) highlight the sensor construction. An 11 lm tall cylindrical air volume with 504 lm radius is enclosed by a 2.25 lm thick polysilicon diaphragm layer. The polysilicon layer has a clamped/clamped boundary condition at the 504 lm radius perimeter. In the outer region of radius 315 lm to 504 lm, the layer is supported by rigid post structures, which prevent the diaphragm from moving. In the center region of radius 0 to 315 lm, no posts exist, and the diaphragm is free to vibrate. Figure 1(c) is a CAD image in
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III. FABRICATION
FIG. 1. (Color online) (a) Labeled SEM of the surface-micromachined, omnidirectional microphone. (b) Labeled CAD cross-section of device. (c) CAD image with diaphragm removed.
which the top diaphragm layer has been removed in order to highlight the post structures and bottom electrodes, which have the same 315 lm radius as the movable portion of the diaphragm. The sensor has dual, concentric bottom electrodes to allow three-port operation. However, in this work, the bottom electrodes where electrically connected to function as a single bottom electrode. The region of the structure with radius less than 315 lm is therefore a conventional variable parallel plate capacitive transducer, with an electrically conductive, pressure-sensitive diaphragm suspended above a rigid bottom electrode. The back cavity of the sensor consists of the air volume directly underneath the movable portion of the diaphragm and also the air volume in the extended cavity region with radius 315–504 lm. Two small openings along the outer perimeter allow the bottom electrode traces to be routed to bond pads near the edge of the chip, as can be seen in Figs. 1(a) and 1(c). The small openings form a low frequency vent to acoustic pressure, similar to a vent intentionally introduced in traditional capacitive MEMS microphones to block DC response to ambient environmental pressure fluctuations. J. Acoust. Soc. Am., Vol. 135, No. 6, June 2014
Key steps of the fabrication process are illustrated in Fig. 2. The process begins with a silicon wafer with a dielectric foundation of 0.63 lm of thermal oxide and 0.80 lm of silicon nitride. A 0.3 lm thick LPCVD polysilicon layer, i.e., poly1, is deposited and patterned to form the bottom electrodes, traces, bond pads, and the base of the posts and sidewalls. The process then alternates between deposition of sacrificial oxide layers, i.e., saccox1-4, and polysilicon layers, i.e., poly2-4, with each layer adding height to the posts and side walls. The last polysilicon layer in the process, poly5, is used to form the top membrane. The 2 lm 2 lm release holes etched in the top membrane allow the sacrificial oxide to be removed from within the microphone structure. To maximize the acoustical resistance of the release holes, structures resembling a drip-pan are fabricated beneath each of the release holes using the poly4 layer. A partial etch into the saccox4 layer, known as a dimple etch, surrounds each release hole and minimizes the space between the poly5 layer and the poly4 drip-pan structures to maximize acoustical resistance. For the particular devices presented in this study, atomic layer deposition of approximately 250 nm of Al2O3 was performed post-process to close the release holes and prevent them from contributing to the acoustic vent resistance. The dimensions of the acoustic vents along the perimeter of the structure are substantially larger than the etch release holes and, therefore, remain open after the atomic layer deposition process, as intended. A final set of SEMs are presented in Fig. 3. Figure 3(a) shows the acoustic vent at two different zoom levels, and Fig. 3(b) shows a zoomed in view of a single post structure within the device. Figure 3(c) shows a labeled side-view SEM of one of the drip-pan structures. Figures 3(b) and 3(c) required destroying a device by cutting with a dicing saw and partially removing the diaphragm prior to taking the SEMs.
IV. DEVICE MODEL AND ELECTROSTATIC RESPONSE
Figure 4 presents a network model superimposed onto the schematic of the device, with pressure and volume velocity as the effort and flow variables, respectively, used in the network. All impedances presented are therefore acoustical impedances. Table I provides values and a description for all elements in the network. The use of an acoustical resistor in series with the cavity compliance is a way to capture the physical trend that the cavity presents compliance in series with the diaphragm at low frequencies and transitions to resistive impedance at higher frequencies. All network elements in Fig. 4 are inherently acoustical except for the diaphragm compliance and mass, which are mechanical parameters that must be transformed into acoustical elements using an effective area. Since the diaphragm is supported along its circumference in a clamped-clamped fashion, the deflection profile is not uniform. The use of a modal coordinate description of the diaphragm deflection provides a rigorous framework for definition of mechanical mass and compliance and for subsequent conversion of these M. L. Kuntzman and N. Hall: Surface-micromachined microphone
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FIG. 2. (Color online) Key steps of fabrication process and labeled cross-section of the finished device.
parameters into acoustical parameters using an effective area. A modal coordinate description of the diaphragm vibration is uðr; tÞ ¼ wðrÞgðtÞ;
(1)
where u is the distributed diaphragm deflection profile and wðrÞ is the first vibration mode of the diaphragm normalized to unity at the center. gðtÞ is therefore the diaphragm deflection amplitude at the center. Equation (1) is a description of the diaphragm vibration in modal coordinates. In modal coordinates, mass, compliance, and modal force have rigorous mathematical definitions.14 Definitions for modal mass 3418
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and compliance are presented in the footnotes accompanying Table I. Modal mass is sometimes referred to as a kineticenergy effective mass, because the kinetic energy is equal to 1 _2 2 mg , as can be verified from the integral definition of modal mass provided in the footnotes to Table I. The modal mass, first-mode resonance frequency, and modal compliance are obtained directly from ANSYS using clamped-clamped boundary conditions for the 315 lm radius diaphragm structure. In electrical equivalent network models, the interface of mechanical and acoustical domains is represented by a transformer with turns ratio equal to the area of the mechanical element. This is easily understood since the volume flow variable, Q [m3 =s], in the acoustical domain is equal to A v, M. L. Kuntzman and N. Hall: Surface-micromachined microphone
FIG. 3. (a) SEM of trace tunnel providing acoustical vent resistance with inset providing higher magnification. (b) SEM of support post with diaphragm partially removed. (c) Side view of drip-pan structure for sealing release holes. The device was cut with a dicing saw to enable the crosssection view for this SEM.
where v is the mechanical velocity of a piston face of area, A. More generally, for non-uniform deformations of mechanÐ _ ef f , where Aef f icalÐ structures, Q ¼ g_ wdA or Q ¼ gA ¼ wdA. Aef f is therefore the turns-ratio used in transforming the diaphragm’s mechanical impedance into acoustical impedance. Specifically, mad ¼ m=A2ef f and Cad ¼ Cm A2ef f , where m is the modal mass and Cm is the mechanical compliance, as summarized in Table I. The cavity compliance and resistance are, in general, frequency-dependent and were calculated using a finite element squeeze film model in ANSYS. Specifically, the modal projection technique in ANSYS was used, which is based on the 2-D Reynolds equation.15 The Reynolds equation is a simplification of the full Navier-Stokes equations and takes into account the compressibility and viscosity of air in the thin gap but disregards inertial effects. The modal projection method projects a vertical velocity profile onto the fluid following Eq. (1) and solves for the scalar pressure in the thin gap using the 2-D Reynolds equation. The complex pressure is then integrated to obtain a modal damping force that has both resistive and reactive components. Figure 5 shows the real and imaginary components of the acoustical film impedance. At low frequencies, the reactive component of the impedance should be very accurately approximated using the well-known lumped element expression for impedance of an acoustical cavity, Za ¼ 1=jxCa;cav with the expression for Ca;cav provided in Table I. This analytical expression for the reactive component of the cavity impedance is also plotted in Fig. 5 and is approximately equal to the value returned by the FEA at low frequencies. For the geometry of the prototype device and at frequencies below 200 kHz, the acoustical film impedance is well approximated by a simple series combination of Ra;cav and Ca;cav . In the pass-band of the sensor, the cavity presents a compliance, and in the pass-band the diaphragm is responsible for 37% of the total acoustic stiffness, with the cavity responsible for 63%. Together, the total simulated center point diaphragm deflection in response to uniformly applied acoustic pressure is 0.40 nm/Pa. Acoustic radiation impedance has also been included in the model using a baffled piston approximation, although the effect is negligible compared to the other elements. To adapt the baffled piston impedance expressions to the case of the non-uniform diaphragm velocity profile, a piston-equivalent effective radius
FIG. 4. (Color online) Network model of device superimposed on a 3D CAD rendering. The effort and flow variables are pressure and volume velocity, respectively. Pacst and Pes represent acoustic and electrostatic actuation, respectively. The voltage sources Pn,Rc and Pn,Rv represent the thermalmechanical pressure noise introduced by the cavity and vent damping elements, respectively.
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TABLE I. Summary of network parameters. Symbol
Description
Notes
Value
Units
Ca,cav Ra,cav Ra,vent ma,vent ma,d
Back cavity compliance Back cavity resistance Vent resistance Vent mass Diaphragm mass
Ca;cav ¼ Vcav =qo c2o a Fitted and compared to FEA resultsb
6.32 1017 2.4 1010 5.58 1013 1.20 106 2.83 104
m3 =Pa Pa s=m3 Pa s=m3 kg=m4 kg=m4
Ca,d
Diaphragm compliance
Za,rad
Radiation impedance
Pacst Pes Pn,Rc
Acoustic input pressure Electrostatic input pressure Noise pressure density of Ra,cav
Pn,Rv
Noise pressure density of Ra,vent
Ra;vent ¼ 12ll=wh3 c ma;vent ¼ qo lw=wh ma;d ¼ m=A2ef f d Za;rad
Ca;d ¼ Cm A2ef f ¼ A2ef f =x2n me ¼ Zo =Aef f 1 2J1 ð2kref f Þ=2kref f f pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn;Rc ¼ 4kb TRa;cav g pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn;Rv ¼ 4kb TRa;vent
1.09 1016
m3 =Pa
-
Pa s=m3
1 1 1.99 105
Pa Pa pffiffiffiffiffiffi Pa= Hz pffiffiffiffiffiffi Pa= Hz
9.58 104
Vcav ¼ 8:77 1012 m3 ; qo ¼ 1:21 kg=m3 is the density of air, and co ¼ 343 m=s is the speed of sound in air. See Fig. 5. c 5 l ¼ 1:86 s is the*viscosity of air; l ¼ 40 lm; w ¼ 20 lm; and h ¼ 2 lm. * Ð Ð Ð 10 kg=m d m¼ qðx; y; zÞwðx; y; zÞ wðx; y; zÞdV ¼ 2:99 1010 kg is the modal mass of the diaphragm. e Cm ¼ 1=x2n m ¼ 0:0103 m=N is the mechanical compliance and m is the modal mass of the diaphragm. f Zo ¼ 415 Pa s=m J1 ðxÞ is a 1st order Bessel function. The imaginary component of the radiation impedance is negligible. g kb ¼ 1:38 1023 kg m2 =K s is the Boltzmann constant, T is temperature. a
b
1 : 1 þ Ca;cav =Ca;d
of the diaphragm is used, denoted reff and defined as the radius of a circular piston that would generate the same volume velocity as the non-uniform diaphragm. It follows that pref2 f ¼ Aef f . The real component of the acoustical radiation impedance is also plotted in Fig. 5. The network model shown in Fig. 4 is used to simulate the center point diaphragm displacement in response to 1 Pa acoustic pressure and 1 Pa electrostatic actuation pressure, as well as the thermal-mechanical self-noise of the device, shown in Fig. 6. The acoustic and electrostatic responses differ only at low frequency. The acoustic response shows a low frequency pole (i.e., lower limiting frequency) common to conventional capacitive MEMS microphones. Analysis of the network in Fig. 4 provides an analytical expression for the pole frequency as
For the particular prototype presented here, fc ¼ 16.5 Hz. The network model is also used to simulate the diaphragm displacement in response to thermal mechanical noise induced by the vent and cavity acoustical resistances. The dynamic frequency response to electrostatic actuation of the diaphragm was measured over a broad frequency range while recording the diaphragm displacement with a high-speed laser Doppler vibrometer (Polytec OFV-505). Electrostatic response characterization has an advantage over acoustic response characterization in that the force is applied only locally to the structure, and it can be applied uniformly over a broad frequency—up to and beyond the
FIG. 5. (Color online) Comparison of fitted and FEA acoustical cavity impedance.
FIG. 6. (Color online) Simulated response to acoustic and electrostatic actuation and displacement due to thermal-mechanical noise of vent and cavity damping elements. Each curve represents the diaphragm displacement in response to one of the voltage sources shown in Fig. 4.
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fc ¼
2pCa;d Ra;vevt
(2)
M. L. Kuntzman and N. Hall: Surface-micromachined microphone
fundamental resonance frequency of the device. The device was biased at 50 V and a small 1 V signal was swept across the device using the tracking generator function of a 2 GHz spectrum analyzer (Rigol DSA815) while the output from the vibrometer was fed back into the spectrum analyzer to record the displacement, as shown in the sketch in Fig. 7. The measured electrostatic frequency response is presented in Fig. 8. The peak in the response occurs at a frequency of 163 kHz, and the response falls to 3 dB below the flat-band compliance at 230 kHz. The device can therefore be expected to measure airborne ultrasound up to 230 kHz frequencies. The simulated acoustic response from Fig. 6 is also superimposed on Fig. 8. While the simulation has excellent agreement with the flat-band sensitivity of 0.4 nm=Pa, the simulation under-predicts the resonance of the device which may be due to neglecting stiffness and stress added by the Al2O3 layer used to seal the release-etch holes, or residual tensile stress in the polysilicon diaphragm layer resulting from fabrication.
V. ACOUSTIC MEASUREMENTS AND SNR CHARACTERISTICS
The schematic of the readout circuit for the device is presented in Fig. 9(a). A bias voltage of 100 V from an AA Lab Systems model A-301 high voltage supply is passed through a passive low pass filter (LPF) network for noise considerations before falling across the device capacitance. A charge amp configuration is used with feedback parameters summarized in the figure. The device capacitance is computed as 0.25 pF, and it is much smaller than parasitic capacitance contained on chip and also in the protoboard amplifier setup, the total of which is estimated as 40 pF. The virtual ground prevents signal attenuation due to Cp, but Cp admits excessive current to ground arising from the voltage noise internal to the op amp, which in turn flows through the feedback network to create a noise at the op amp output. Figure 9(b) presents the small-signal AC circuit resulting upon application of the bias. Relevant noise sources are included along with the expression for the charge generated by the variable capacitance in response to diaphragm displacements. Transient ultrasonic waveforms were recorded to verify device functionality. Figure 10 presents a schematic of the
FIG. 7. (Color online) Sketch of setup used in electrostatic sensitivity measurements. The device is actuated with a swept sine signal applied from the spectrum analyzer while the diaphragm velocity is measured by the Laser Doppler Vibrometer (LDV). An impedance buffer is used to interface with the 50X input terminal of the spectrum analyzer. J. Acoust. Soc. Am., Vol. 135, No. 6, June 2014
FIG. 8. (Color online) The measured and simulated electrostatic response of the device, converted to pressure sensitivity using the effective diaphragm area and applied electrostatic force.
setup in which a narrowband piezoelectric buzzer with a resonance at 30.4 kHz was used to generate a finite duration tone burst. The input waveform was captured with an oscilloscope and is depicted in Fig. 11, along with the acoustic waveform capture by a GRAS microphone model 40AC. Figure 11 also includes the ultrasonic waveform as measured by the device under study. To verify the absence of any electromagnetic coupling, the sound was blocked using a metal plate, and it was confirmed that no signals were present. Further, the time delay between the voltage input to the
FIG. 9. (Color online) (a) Schematic of the readout circuit used for the acoustic measurements. The bias voltage was applied to the device though an RC lowpass filter to remove electromagnetic interference and noise from the bias supply. A parasitic capacitance of approximately 40 pF was inferred from noise measurements (shown in Fig. 12). (b) Schematic of amplifier with the sensor modeled as a current source. M. L. Kuntzman and N. Hall: Surface-micromachined microphone
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FIG. 10. (Color online) Sketch of experimental setup for acoustic ultrasound captures.
buzzer and the measured acoustic response is as expected given the 90 mm distance noted in Fig. 10. Referring to Fig. 11, the start of the input to the buzzer is 29.8 ls, while the start of the device under test response is 271.4 ls, providing a time-of-flight measurement of 241.6 ls. Using 344 m/s for speed of sound, 83 mm distance is computed which is consistent with the rough measurement made of 90 mm using a ruler in the lab. The simulated amplifier output in response to 1 Pa sound pressure is presented in Fig. 12, assuming a device sensitivity equal to the flat-band value. The particular set of feedback values in this study results in a transimpedance amplifier (TIA) region below 482 Hz, and a charge amplifier region above 482 Hz and through the pass-band of the device. A quantitative measure of device sensitivity was performed at 2256 Hz using the same setup presented in Fig. 10. Figure 13(a) presents the FFT of the GRAS and microphone under test output in response to a continuous wave signal. The GRAS has a known calibration scale factor equal to 14.5 mV/Pa. From Fig. 13(a), the signals from the GRAS and the device under test are 1.25 mV and 13.7 lV, respectively, implying a device sensitivity equal to Sacst ¼
Vdevice 13:7lV 14:5 mV=Pa Sref ¼ Vref 1:25 mV
¼ 0:159 mV=Pa:
(3)
FIG. 12. (Color online) SNR simulated from measured flat-band sensitivity compared to measured and simulate total noise and contributions of each noise source.
From the simulation in Fig. 12, the simulated sensitivity at 2256 Hz is 0.167 mV/Pa, a difference of 4.8% from the measured value. Figure 12 also presents the measured and simulated noise appearing at the amplifier output. The noise is dominated by the feedback resistor thermal noise at low frequency and by amplifier voltage noise at high frequency. These trends are identical to those presented by Martin et al.,9 who also used a charge amp readout configuration for a broadband capacitive MEMS acoustic sensor. As noted by Martin, noise is this region is directly proportional to Cp, so future designs will benefit from reducing on-chip parasitic capacitance. The simulated thermal-mechanical noise spectrum at the amplifier output is included for completeness, but this noise source does not dominate the output noise across any region of the spectrum. A slightly smaller test bed in the form of a circular PCB with 3 in. diameter was created for testing the frequency response over a broader range of frequencies. The modified setup utilized the same circuit configuration as presented in Fig. 9, but with a bias voltage of 50 V and component values of Cf ¼ 10 pF and Rf ¼ 50 MX. A swept frequency response over the range 700 Hz to 10 kHz was measured in an anechoic facility using an ADAM A5 studio monitor as the acoustic source and is presented in Fig. 13(b) along with the simulated response. A spurious resonance of the printed circuit board (PCB)-based package occurs near 2 kHz and corrupts the measurement in this regime. In the remaining frequency range shown, the measurement is within 62.5 dB of the simulation. The imperfections of the measurement in Fig. 13 illustrate the importance of acute attention to packaging details in future implementations of the device. VI. DISCUSSION AND CONCLUSION
FIG. 11. (Color online) Time-of-flight ultrasound measurement providing qualitative demonstration of functionality as an acoustic sensor. 3422
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Figure 14 presents the pressure-input referred noise of the microphone, obtained by dividing the noise pffiffiffiffiffiffiby the device sensitivity. At 1 kHz, the noise is 4.5mPa= Hz (47 dB in a pffiffiffiffiffiffi 1 Hz bin), and 0.80mPa= Hz (32 dB) in the flat region M. L. Kuntzman and N. Hall: Surface-micromachined microphone
FIG. 13. (Color online) Acoustic sensitivity measurements. (a) Single frequency calibration performed at 2256 Hz. (b) Over the 700 Hz to 10 kHz range, using an amplifier configuration in which Cf ¼ 10 pF, Rf ¼ 50 MX, and Vbias ¼ 50 V.
above 10 kHz. For applications benefiting from lower noise floors, it is interesting to explore limits of the sensor þ charge amp configuration. Figure 14 also plots the simulated noise resulting from a design in which parasitic capacitance has been successfully reduced to a value of 1.0 pF. In this case, noise in the flat region is reduced to 9.5 dB (1 Hz bin), but this improvement alone has no impact on the noise at 1 kHz. An increase in feedback resistance from 150 pMX ffiffiffiffiffiffi to 1 GX reduces the noise at 1 kHz down to 1.7mPa= Hz, or 38.6 dB. This case is also presented in Fig. 14. Additional improvements would need to arise from the use of multiple sensors configured in close proximity to create an array summed in parallel. The final case shown in Fig. 14 presents the simulated noise assuming four sensorspsummed in paralffiffiffiffiffiffi lel. The noise in this case is 0.44mPa= Hz (26.8 dB) at 1 kHz and 16.2 uPa (1.83 dB) above 30 kHz. Considering the radius of the prototype is 504 lm, the hypothetical four
sensor array would occupy approximately 2 mm 2 mm area. The measured noise figures for the fabricated prototype fall within the range of results reported by other sensor technologies as summarized by Martin et al.9 It is difficult to make a direct sensor-to-sensor comparison based on noise alone, since many other factors are important depending on the device application (e.g., bandwidth of operation, size, and dynamic range). Other non-quantifiable constraints also influence the choice of broadband sensor technology. The present work was partially motivated by a desire to develop a purely surface-micromachined solution to maintain compatibility with a fabrication process already established for a vacuum-sealed pressure-gradient sensor.12 Future work consists of integration of omnidirectional and pressure-gradient surface-micromachined sensors on a common silicon die. AKNOWLEDGMENTS
The authors would like to thank Nishshanka N. HewaKasakarage for aiding in the preparation of Figs. 1 and 3 and Karen D. Kirk for aiding in the mask file layout for this device. This work is supported by DARPA Grant # N6600112-1-4222.
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FIG. 14. (Color online) Simulated improvement in pressure-referred input noise with several amplifier configurations. J. Acoust. Soc. Am., Vol. 135, No. 6, June 2014
S. Hiryu, T. Hagino, H. Riquimaroux, and Y. Watanabe, “Echo-intensity compensation in echolocating bats (Pipistrellus abramus) during flight measured by a telemetry microphone,” J. Acoust. Soc. Am. 121, 1749–1757 (2007). 2 R. Stoughton, “Measurements of small-caliber ballistic shock waves in air,” J. Acoust. Soc. Am. 102, 781–787 (1997). 3 Z. J. Zhou, L. Rufer, and M. Wong, “Aero-acoustic microphone with layer-transferred single-crystal silicon piezoresistors,” in Transducers 2009 (IEEE, Denver, CO, 2009), pp. 1916–1919. 4 Z. J. Zhou, L. Rufer, E. Salze, P. Yuldashev, S. Ollivier, and M. Wong, “Bulk micro-machined wide-band aero-acoustic microphone and its application to acoustic ranging,” J. Micromech. Microeng. 23, 105006 (2013). 5 M. D. Williams, B. A. Griffin, T. N. Reagan, J. R. Underbrink, and M. Sheplak, “An AlN MEMS Piezoelectric Microphone for M. L. Kuntzman and N. Hall: Surface-micromachined microphone
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Aeroacoustic Applications,” J. Microelectromech. Syst. 21, 270–283 (2012). 6 S. Horowitz, T. Nishida, L. Cattafesta, and M. Sheplak, “Development of a micromachined piezoelectric microphone for aeroacoustics applications,” J. Acoust. Soc. Am. 122, 3428–3436 (2007). 7 K. Kadirvel, T. Robert, S. Horowitz, L. Hunt, M. Sheplak, and T. Nishida, “Design and characterization of MEMS optical microphone for aeroacoustic measurement,” in 42nd Aerospace Sciences Meeting & Exhibit, Reno, NV (January 5–8, 2004), pp. 2–10. 8 E. Radcliffe, A. Naguib, and J. W. M. Humphreys, “A novel design of a feedback-controlled optical microphone for aeroacoustics research,” Meas. Sci. Technol. 21, 105208 (2010). 9 D. T. Martin, J. Liu, K. Kadirvel, R. M. Fox, M. Sheplak, and T. Nishida, “A micromachined dual-backplate capacitive microphone for aeroacoustic measurements,” J. Microelectromech. Syst. 16, 1289–1302 (2007). 10 S. T. Hansen, A. S. Ergun, W. Liou, B. A. Auld, and B. T. Khuri-Yakub, “Wideband micromachined capacitive microphones with radio frequency detection,” J. Acoust. Soc. Am. 116, 828–842 (2004).
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S. T. Hansen, A. S. Ergun, and B. T. Khuri-Yakub, “Improved modeling and design of microphones using radio frequency detection with capacitive micromachined ultrasonic transducers,” in 2001 IEEE Ultrasonics Symposium (IEEE, 2001), Vol. 2, pp. 961–964. 12 M. L. Kuntzman and N. A. Hall, “Rotational capacitive micromachined ultrasonic transducers (cMUTS),” J. Microelectromech. Syst. 23(1), 1–3 (2014). 13 P. R. Scheeper, B. Nordstrand, J. O. Gullov, B. Liu, T. Clasuen, L. Midjord, and T. Storgaard-Larsen, “A new measurement microphone based on MEMS technology,” J. Microelectromech. Syst. 12, 880–891 (2003). 14 J. H. Ginsberg, Mechanical and Structural Vibrations: Theory and Applications (John Wiley and Sons, New York, 2001), pp. 219–591. 15 J. E. Mehner, W. Doetzel, B. Schauwecker, and D. Ostergaard, “Reduced order modeling of fluid structural interactions in MEMS based on model projection techniques,” in 12th International Conference on Transducers, Solid-State Sensors, Actuators and Microsystems (IEEE, 2003), Vol. 2, pp. 1840–1843.
M. L. Kuntzman and N. Hall: Surface-micromachined microphone
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(Received 5 November 2013; revised 5 February 2014; accepted 14 April 2014) A surface micromachined microphone is presented with 230 kHz bandwidth. The structure uses a 2.25 lm thick, 315 lm radius polysilicon diaphragm suspended above an 11 lm gap to form a variable parallel-plate capacitance. The back cavity of the microphone consists of the 11 lm thick air volume immediately behind the moving diaphragm and also an extended lateral cavity with a radius of 504 lm. The dynamic frequency response of the sensor in response to electrostatic signals is presented using laser Doppler vibrometry and indicates a system compliance of 0.4 nm/Pa in the flat-band of the response. The sensor is configured for acoustic signal detection using a charge amplifier, and pffiffiffiffiffiffisignal-to-noise ratio measurements and simulations are presented. A resolution of 0.80 mPa= Hz (32 dB sound pressure level in a 1 Hz bin) is achieved in the flat-band portion of the response extending from 10 kHz to 230 kHz. The proposed sensor design is motivated by defense and intelligence gathering applications that require broadband, airborne signal detection. C 2014 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4874620] V PACS number(s): 43.38.Bs, 43.38.Gy, 43.38.Kb, 43.38.Lc [MS]
I. INTRODUCTION
Microphones with bandwidth extending beyond the audio range and up to hundreds of kHz and beyond have applications in several fields. In aeroacoustics, measurements with broadband microphone arrays and dynamic pressure sensors are used to study sources of noise of various aircraft components and to study turbulent boundary layers. Acoustic cameras utilizing nearfield holography techniques have been developed to study noise sources in many industrial noise control applications including automotive and manufacturing sectors. Broadband microphones are also used in biological studies. In recent studies, microphones were mounted atop bats to measure echolocation pulse intensity.1 The measurement range of interest in this study was 20–192 kHz. Broadband acoustic sensors are also applied in military and defense applications; including use in acoustic fingerprinting applications and sniper detection systems where muzzle blasts with spectral content up to 1 MHz is measured.2 Technologies used to address broadband microphone design include piezoresistive,3,4 piezoelectric,5,6 optical,7,8 and capacitive readout.9–11 Martin et al.9 summarizes and compares several recent works in this field. Because each application has unique requirements, not one technology fits all applications. Partial motivation for the present work is to develop an omnidirectional microphone that is compatible with a previously developed pressure gradient sensor,12 so that the sensors can be fabricated together on a single silicon die using the same surface-micromachining fabrication process to realize a miniature, broadband sensor array for acoustic localization applications.
a)
Author to whom correspondence should be addressed. Electronic mail: [email protected]
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Pages: 3416–3424
This work presents an overview of the construction of the sensor, followed by presentation of a dynamic device model and verification using electrostatic actuation and laser Doppler vibrometry (LDV) measurements of the microphone diaphragm. Acoustic measurements are then presented along with signal-to-noise ratio (SNR) characterization. Generally speaking, in comparison to conventional instrumentation microphones, the purely surface micromachined acoustic sensor introduced may have advantages of small size and lower cost fabrication due to the simple surface-micromachined construction. The sensor uses materials stable to relatively high temperatures compared to lead zirconate titanate (PZT) and other Curietemperature limited ceramic based microphones, which may offer an advantage for some applications. The sensor fabrication could also easily be adapted to fabrication using silicon carbide, diamond, or other materials well suited for high-temperature and harsh environment applications. Compared to bulk-micromachined capacitive broadband microphones,9,13 the sensor introduced here has perhaps simpler fabrication but the disadvantage of smaller capacitance and higher noise. II. DESCRIPTION OF SENSOR
A scanning electron micrograph (SEM) of a fabricated prototype is presented in Fig. 1(a), and 3D CAD sections in Figs. 1(b) and 1(c) highlight the sensor construction. An 11 lm tall cylindrical air volume with 504 lm radius is enclosed by a 2.25 lm thick polysilicon diaphragm layer. The polysilicon layer has a clamped/clamped boundary condition at the 504 lm radius perimeter. In the outer region of radius 315 lm to 504 lm, the layer is supported by rigid post structures, which prevent the diaphragm from moving. In the center region of radius 0 to 315 lm, no posts exist, and the diaphragm is free to vibrate. Figure 1(c) is a CAD image in
0001-4966/2014/135(6)/3416/9/$30.00
C 2014 Acoustical Society of America V
III. FABRICATION
FIG. 1. (Color online) (a) Labeled SEM of the surface-micromachined, omnidirectional microphone. (b) Labeled CAD cross-section of device. (c) CAD image with diaphragm removed.
which the top diaphragm layer has been removed in order to highlight the post structures and bottom electrodes, which have the same 315 lm radius as the movable portion of the diaphragm. The sensor has dual, concentric bottom electrodes to allow three-port operation. However, in this work, the bottom electrodes where electrically connected to function as a single bottom electrode. The region of the structure with radius less than 315 lm is therefore a conventional variable parallel plate capacitive transducer, with an electrically conductive, pressure-sensitive diaphragm suspended above a rigid bottom electrode. The back cavity of the sensor consists of the air volume directly underneath the movable portion of the diaphragm and also the air volume in the extended cavity region with radius 315–504 lm. Two small openings along the outer perimeter allow the bottom electrode traces to be routed to bond pads near the edge of the chip, as can be seen in Figs. 1(a) and 1(c). The small openings form a low frequency vent to acoustic pressure, similar to a vent intentionally introduced in traditional capacitive MEMS microphones to block DC response to ambient environmental pressure fluctuations. J. Acoust. Soc. Am., Vol. 135, No. 6, June 2014
Key steps of the fabrication process are illustrated in Fig. 2. The process begins with a silicon wafer with a dielectric foundation of 0.63 lm of thermal oxide and 0.80 lm of silicon nitride. A 0.3 lm thick LPCVD polysilicon layer, i.e., poly1, is deposited and patterned to form the bottom electrodes, traces, bond pads, and the base of the posts and sidewalls. The process then alternates between deposition of sacrificial oxide layers, i.e., saccox1-4, and polysilicon layers, i.e., poly2-4, with each layer adding height to the posts and side walls. The last polysilicon layer in the process, poly5, is used to form the top membrane. The 2 lm 2 lm release holes etched in the top membrane allow the sacrificial oxide to be removed from within the microphone structure. To maximize the acoustical resistance of the release holes, structures resembling a drip-pan are fabricated beneath each of the release holes using the poly4 layer. A partial etch into the saccox4 layer, known as a dimple etch, surrounds each release hole and minimizes the space between the poly5 layer and the poly4 drip-pan structures to maximize acoustical resistance. For the particular devices presented in this study, atomic layer deposition of approximately 250 nm of Al2O3 was performed post-process to close the release holes and prevent them from contributing to the acoustic vent resistance. The dimensions of the acoustic vents along the perimeter of the structure are substantially larger than the etch release holes and, therefore, remain open after the atomic layer deposition process, as intended. A final set of SEMs are presented in Fig. 3. Figure 3(a) shows the acoustic vent at two different zoom levels, and Fig. 3(b) shows a zoomed in view of a single post structure within the device. Figure 3(c) shows a labeled side-view SEM of one of the drip-pan structures. Figures 3(b) and 3(c) required destroying a device by cutting with a dicing saw and partially removing the diaphragm prior to taking the SEMs.
IV. DEVICE MODEL AND ELECTROSTATIC RESPONSE
Figure 4 presents a network model superimposed onto the schematic of the device, with pressure and volume velocity as the effort and flow variables, respectively, used in the network. All impedances presented are therefore acoustical impedances. Table I provides values and a description for all elements in the network. The use of an acoustical resistor in series with the cavity compliance is a way to capture the physical trend that the cavity presents compliance in series with the diaphragm at low frequencies and transitions to resistive impedance at higher frequencies. All network elements in Fig. 4 are inherently acoustical except for the diaphragm compliance and mass, which are mechanical parameters that must be transformed into acoustical elements using an effective area. Since the diaphragm is supported along its circumference in a clamped-clamped fashion, the deflection profile is not uniform. The use of a modal coordinate description of the diaphragm deflection provides a rigorous framework for definition of mechanical mass and compliance and for subsequent conversion of these M. L. Kuntzman and N. Hall: Surface-micromachined microphone
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FIG. 2. (Color online) Key steps of fabrication process and labeled cross-section of the finished device.
parameters into acoustical parameters using an effective area. A modal coordinate description of the diaphragm vibration is uðr; tÞ ¼ wðrÞgðtÞ;
(1)
where u is the distributed diaphragm deflection profile and wðrÞ is the first vibration mode of the diaphragm normalized to unity at the center. gðtÞ is therefore the diaphragm deflection amplitude at the center. Equation (1) is a description of the diaphragm vibration in modal coordinates. In modal coordinates, mass, compliance, and modal force have rigorous mathematical definitions.14 Definitions for modal mass 3418
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and compliance are presented in the footnotes accompanying Table I. Modal mass is sometimes referred to as a kineticenergy effective mass, because the kinetic energy is equal to 1 _2 2 mg , as can be verified from the integral definition of modal mass provided in the footnotes to Table I. The modal mass, first-mode resonance frequency, and modal compliance are obtained directly from ANSYS using clamped-clamped boundary conditions for the 315 lm radius diaphragm structure. In electrical equivalent network models, the interface of mechanical and acoustical domains is represented by a transformer with turns ratio equal to the area of the mechanical element. This is easily understood since the volume flow variable, Q [m3 =s], in the acoustical domain is equal to A v, M. L. Kuntzman and N. Hall: Surface-micromachined microphone
FIG. 3. (a) SEM of trace tunnel providing acoustical vent resistance with inset providing higher magnification. (b) SEM of support post with diaphragm partially removed. (c) Side view of drip-pan structure for sealing release holes. The device was cut with a dicing saw to enable the crosssection view for this SEM.
where v is the mechanical velocity of a piston face of area, A. More generally, for non-uniform deformations of mechanÐ _ ef f , where Aef f icalÐ structures, Q ¼ g_ wdA or Q ¼ gA ¼ wdA. Aef f is therefore the turns-ratio used in transforming the diaphragm’s mechanical impedance into acoustical impedance. Specifically, mad ¼ m=A2ef f and Cad ¼ Cm A2ef f , where m is the modal mass and Cm is the mechanical compliance, as summarized in Table I. The cavity compliance and resistance are, in general, frequency-dependent and were calculated using a finite element squeeze film model in ANSYS. Specifically, the modal projection technique in ANSYS was used, which is based on the 2-D Reynolds equation.15 The Reynolds equation is a simplification of the full Navier-Stokes equations and takes into account the compressibility and viscosity of air in the thin gap but disregards inertial effects. The modal projection method projects a vertical velocity profile onto the fluid following Eq. (1) and solves for the scalar pressure in the thin gap using the 2-D Reynolds equation. The complex pressure is then integrated to obtain a modal damping force that has both resistive and reactive components. Figure 5 shows the real and imaginary components of the acoustical film impedance. At low frequencies, the reactive component of the impedance should be very accurately approximated using the well-known lumped element expression for impedance of an acoustical cavity, Za ¼ 1=jxCa;cav with the expression for Ca;cav provided in Table I. This analytical expression for the reactive component of the cavity impedance is also plotted in Fig. 5 and is approximately equal to the value returned by the FEA at low frequencies. For the geometry of the prototype device and at frequencies below 200 kHz, the acoustical film impedance is well approximated by a simple series combination of Ra;cav and Ca;cav . In the pass-band of the sensor, the cavity presents a compliance, and in the pass-band the diaphragm is responsible for 37% of the total acoustic stiffness, with the cavity responsible for 63%. Together, the total simulated center point diaphragm deflection in response to uniformly applied acoustic pressure is 0.40 nm/Pa. Acoustic radiation impedance has also been included in the model using a baffled piston approximation, although the effect is negligible compared to the other elements. To adapt the baffled piston impedance expressions to the case of the non-uniform diaphragm velocity profile, a piston-equivalent effective radius
FIG. 4. (Color online) Network model of device superimposed on a 3D CAD rendering. The effort and flow variables are pressure and volume velocity, respectively. Pacst and Pes represent acoustic and electrostatic actuation, respectively. The voltage sources Pn,Rc and Pn,Rv represent the thermalmechanical pressure noise introduced by the cavity and vent damping elements, respectively.
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TABLE I. Summary of network parameters. Symbol
Description
Notes
Value
Units
Ca,cav Ra,cav Ra,vent ma,vent ma,d
Back cavity compliance Back cavity resistance Vent resistance Vent mass Diaphragm mass
Ca;cav ¼ Vcav =qo c2o a Fitted and compared to FEA resultsb
6.32 1017 2.4 1010 5.58 1013 1.20 106 2.83 104
m3 =Pa Pa s=m3 Pa s=m3 kg=m4 kg=m4
Ca,d
Diaphragm compliance
Za,rad
Radiation impedance
Pacst Pes Pn,Rc
Acoustic input pressure Electrostatic input pressure Noise pressure density of Ra,cav
Pn,Rv
Noise pressure density of Ra,vent
Ra;vent ¼ 12ll=wh3 c ma;vent ¼ qo lw=wh ma;d ¼ m=A2ef f d Za;rad
Ca;d ¼ Cm A2ef f ¼ A2ef f =x2n me ¼ Zo =Aef f 1 2J1 ð2kref f Þ=2kref f f pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn;Rc ¼ 4kb TRa;cav g pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn;Rv ¼ 4kb TRa;vent
1.09 1016
m3 =Pa
-
Pa s=m3
1 1 1.99 105
Pa Pa pffiffiffiffiffiffi Pa= Hz pffiffiffiffiffiffi Pa= Hz
9.58 104
Vcav ¼ 8:77 1012 m3 ; qo ¼ 1:21 kg=m3 is the density of air, and co ¼ 343 m=s is the speed of sound in air. See Fig. 5. c 5 l ¼ 1:86 s is the*viscosity of air; l ¼ 40 lm; w ¼ 20 lm; and h ¼ 2 lm. * Ð Ð Ð 10 kg=m d m¼ qðx; y; zÞwðx; y; zÞ wðx; y; zÞdV ¼ 2:99 1010 kg is the modal mass of the diaphragm. e Cm ¼ 1=x2n m ¼ 0:0103 m=N is the mechanical compliance and m is the modal mass of the diaphragm. f Zo ¼ 415 Pa s=m J1 ðxÞ is a 1st order Bessel function. The imaginary component of the radiation impedance is negligible. g kb ¼ 1:38 1023 kg m2 =K s is the Boltzmann constant, T is temperature. a
b
1 : 1 þ Ca;cav =Ca;d
of the diaphragm is used, denoted reff and defined as the radius of a circular piston that would generate the same volume velocity as the non-uniform diaphragm. It follows that pref2 f ¼ Aef f . The real component of the acoustical radiation impedance is also plotted in Fig. 5. The network model shown in Fig. 4 is used to simulate the center point diaphragm displacement in response to 1 Pa acoustic pressure and 1 Pa electrostatic actuation pressure, as well as the thermal-mechanical self-noise of the device, shown in Fig. 6. The acoustic and electrostatic responses differ only at low frequency. The acoustic response shows a low frequency pole (i.e., lower limiting frequency) common to conventional capacitive MEMS microphones. Analysis of the network in Fig. 4 provides an analytical expression for the pole frequency as
For the particular prototype presented here, fc ¼ 16.5 Hz. The network model is also used to simulate the diaphragm displacement in response to thermal mechanical noise induced by the vent and cavity acoustical resistances. The dynamic frequency response to electrostatic actuation of the diaphragm was measured over a broad frequency range while recording the diaphragm displacement with a high-speed laser Doppler vibrometer (Polytec OFV-505). Electrostatic response characterization has an advantage over acoustic response characterization in that the force is applied only locally to the structure, and it can be applied uniformly over a broad frequency—up to and beyond the
FIG. 5. (Color online) Comparison of fitted and FEA acoustical cavity impedance.
FIG. 6. (Color online) Simulated response to acoustic and electrostatic actuation and displacement due to thermal-mechanical noise of vent and cavity damping elements. Each curve represents the diaphragm displacement in response to one of the voltage sources shown in Fig. 4.
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fc ¼
2pCa;d Ra;vevt
(2)
M. L. Kuntzman and N. Hall: Surface-micromachined microphone
fundamental resonance frequency of the device. The device was biased at 50 V and a small 1 V signal was swept across the device using the tracking generator function of a 2 GHz spectrum analyzer (Rigol DSA815) while the output from the vibrometer was fed back into the spectrum analyzer to record the displacement, as shown in the sketch in Fig. 7. The measured electrostatic frequency response is presented in Fig. 8. The peak in the response occurs at a frequency of 163 kHz, and the response falls to 3 dB below the flat-band compliance at 230 kHz. The device can therefore be expected to measure airborne ultrasound up to 230 kHz frequencies. The simulated acoustic response from Fig. 6 is also superimposed on Fig. 8. While the simulation has excellent agreement with the flat-band sensitivity of 0.4 nm=Pa, the simulation under-predicts the resonance of the device which may be due to neglecting stiffness and stress added by the Al2O3 layer used to seal the release-etch holes, or residual tensile stress in the polysilicon diaphragm layer resulting from fabrication.
V. ACOUSTIC MEASUREMENTS AND SNR CHARACTERISTICS
The schematic of the readout circuit for the device is presented in Fig. 9(a). A bias voltage of 100 V from an AA Lab Systems model A-301 high voltage supply is passed through a passive low pass filter (LPF) network for noise considerations before falling across the device capacitance. A charge amp configuration is used with feedback parameters summarized in the figure. The device capacitance is computed as 0.25 pF, and it is much smaller than parasitic capacitance contained on chip and also in the protoboard amplifier setup, the total of which is estimated as 40 pF. The virtual ground prevents signal attenuation due to Cp, but Cp admits excessive current to ground arising from the voltage noise internal to the op amp, which in turn flows through the feedback network to create a noise at the op amp output. Figure 9(b) presents the small-signal AC circuit resulting upon application of the bias. Relevant noise sources are included along with the expression for the charge generated by the variable capacitance in response to diaphragm displacements. Transient ultrasonic waveforms were recorded to verify device functionality. Figure 10 presents a schematic of the
FIG. 7. (Color online) Sketch of setup used in electrostatic sensitivity measurements. The device is actuated with a swept sine signal applied from the spectrum analyzer while the diaphragm velocity is measured by the Laser Doppler Vibrometer (LDV). An impedance buffer is used to interface with the 50X input terminal of the spectrum analyzer. J. Acoust. Soc. Am., Vol. 135, No. 6, June 2014
FIG. 8. (Color online) The measured and simulated electrostatic response of the device, converted to pressure sensitivity using the effective diaphragm area and applied electrostatic force.
setup in which a narrowband piezoelectric buzzer with a resonance at 30.4 kHz was used to generate a finite duration tone burst. The input waveform was captured with an oscilloscope and is depicted in Fig. 11, along with the acoustic waveform capture by a GRAS microphone model 40AC. Figure 11 also includes the ultrasonic waveform as measured by the device under study. To verify the absence of any electromagnetic coupling, the sound was blocked using a metal plate, and it was confirmed that no signals were present. Further, the time delay between the voltage input to the
FIG. 9. (Color online) (a) Schematic of the readout circuit used for the acoustic measurements. The bias voltage was applied to the device though an RC lowpass filter to remove electromagnetic interference and noise from the bias supply. A parasitic capacitance of approximately 40 pF was inferred from noise measurements (shown in Fig. 12). (b) Schematic of amplifier with the sensor modeled as a current source. M. L. Kuntzman and N. Hall: Surface-micromachined microphone
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FIG. 10. (Color online) Sketch of experimental setup for acoustic ultrasound captures.
buzzer and the measured acoustic response is as expected given the 90 mm distance noted in Fig. 10. Referring to Fig. 11, the start of the input to the buzzer is 29.8 ls, while the start of the device under test response is 271.4 ls, providing a time-of-flight measurement of 241.6 ls. Using 344 m/s for speed of sound, 83 mm distance is computed which is consistent with the rough measurement made of 90 mm using a ruler in the lab. The simulated amplifier output in response to 1 Pa sound pressure is presented in Fig. 12, assuming a device sensitivity equal to the flat-band value. The particular set of feedback values in this study results in a transimpedance amplifier (TIA) region below 482 Hz, and a charge amplifier region above 482 Hz and through the pass-band of the device. A quantitative measure of device sensitivity was performed at 2256 Hz using the same setup presented in Fig. 10. Figure 13(a) presents the FFT of the GRAS and microphone under test output in response to a continuous wave signal. The GRAS has a known calibration scale factor equal to 14.5 mV/Pa. From Fig. 13(a), the signals from the GRAS and the device under test are 1.25 mV and 13.7 lV, respectively, implying a device sensitivity equal to Sacst ¼
Vdevice 13:7lV 14:5 mV=Pa Sref ¼ Vref 1:25 mV
¼ 0:159 mV=Pa:
(3)
FIG. 12. (Color online) SNR simulated from measured flat-band sensitivity compared to measured and simulate total noise and contributions of each noise source.
From the simulation in Fig. 12, the simulated sensitivity at 2256 Hz is 0.167 mV/Pa, a difference of 4.8% from the measured value. Figure 12 also presents the measured and simulated noise appearing at the amplifier output. The noise is dominated by the feedback resistor thermal noise at low frequency and by amplifier voltage noise at high frequency. These trends are identical to those presented by Martin et al.,9 who also used a charge amp readout configuration for a broadband capacitive MEMS acoustic sensor. As noted by Martin, noise is this region is directly proportional to Cp, so future designs will benefit from reducing on-chip parasitic capacitance. The simulated thermal-mechanical noise spectrum at the amplifier output is included for completeness, but this noise source does not dominate the output noise across any region of the spectrum. A slightly smaller test bed in the form of a circular PCB with 3 in. diameter was created for testing the frequency response over a broader range of frequencies. The modified setup utilized the same circuit configuration as presented in Fig. 9, but with a bias voltage of 50 V and component values of Cf ¼ 10 pF and Rf ¼ 50 MX. A swept frequency response over the range 700 Hz to 10 kHz was measured in an anechoic facility using an ADAM A5 studio monitor as the acoustic source and is presented in Fig. 13(b) along with the simulated response. A spurious resonance of the printed circuit board (PCB)-based package occurs near 2 kHz and corrupts the measurement in this regime. In the remaining frequency range shown, the measurement is within 62.5 dB of the simulation. The imperfections of the measurement in Fig. 13 illustrate the importance of acute attention to packaging details in future implementations of the device. VI. DISCUSSION AND CONCLUSION
FIG. 11. (Color online) Time-of-flight ultrasound measurement providing qualitative demonstration of functionality as an acoustic sensor. 3422
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Figure 14 presents the pressure-input referred noise of the microphone, obtained by dividing the noise pffiffiffiffiffiffiby the device sensitivity. At 1 kHz, the noise is 4.5mPa= Hz (47 dB in a pffiffiffiffiffiffi 1 Hz bin), and 0.80mPa= Hz (32 dB) in the flat region M. L. Kuntzman and N. Hall: Surface-micromachined microphone
FIG. 13. (Color online) Acoustic sensitivity measurements. (a) Single frequency calibration performed at 2256 Hz. (b) Over the 700 Hz to 10 kHz range, using an amplifier configuration in which Cf ¼ 10 pF, Rf ¼ 50 MX, and Vbias ¼ 50 V.
above 10 kHz. For applications benefiting from lower noise floors, it is interesting to explore limits of the sensor þ charge amp configuration. Figure 14 also plots the simulated noise resulting from a design in which parasitic capacitance has been successfully reduced to a value of 1.0 pF. In this case, noise in the flat region is reduced to 9.5 dB (1 Hz bin), but this improvement alone has no impact on the noise at 1 kHz. An increase in feedback resistance from 150 pMX ffiffiffiffiffiffi to 1 GX reduces the noise at 1 kHz down to 1.7mPa= Hz, or 38.6 dB. This case is also presented in Fig. 14. Additional improvements would need to arise from the use of multiple sensors configured in close proximity to create an array summed in parallel. The final case shown in Fig. 14 presents the simulated noise assuming four sensorspsummed in paralffiffiffiffiffiffi lel. The noise in this case is 0.44mPa= Hz (26.8 dB) at 1 kHz and 16.2 uPa (1.83 dB) above 30 kHz. Considering the radius of the prototype is 504 lm, the hypothetical four
sensor array would occupy approximately 2 mm 2 mm area. The measured noise figures for the fabricated prototype fall within the range of results reported by other sensor technologies as summarized by Martin et al.9 It is difficult to make a direct sensor-to-sensor comparison based on noise alone, since many other factors are important depending on the device application (e.g., bandwidth of operation, size, and dynamic range). Other non-quantifiable constraints also influence the choice of broadband sensor technology. The present work was partially motivated by a desire to develop a purely surface-micromachined solution to maintain compatibility with a fabrication process already established for a vacuum-sealed pressure-gradient sensor.12 Future work consists of integration of omnidirectional and pressure-gradient surface-micromachined sensors on a common silicon die. AKNOWLEDGMENTS
The authors would like to thank Nishshanka N. HewaKasakarage for aiding in the preparation of Figs. 1 and 3 and Karen D. Kirk for aiding in the mask file layout for this device. This work is supported by DARPA Grant # N6600112-1-4222.
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FIG. 14. (Color online) Simulated improvement in pressure-referred input noise with several amplifier configurations. J. Acoust. Soc. Am., Vol. 135, No. 6, June 2014
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M. L. Kuntzman and N. Hall: Surface-micromachined microphone
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