A Micromachined Dual-Backplate Capacitive ... - IEEE Xplore

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 16, NO. 6, DECEMBER 2007

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A Micromachined Dual-Backplate Capacitive Microphone for Aeroacoustic Measurements David T. Martin, Jian Liu, Karthik Kadirvel, Robert M. Fox, Mark Sheplak, and Toshikazu Nishida

Abstract—This paper presents the development of a micromachined dual-backplate capacitive microphone for aeroacoustic measurements. The device theory, fabrication, and characterization are discussed. The microphone is fabricated using the five-layer planarized-polysilicon SUMMiT V process at Sandia National Laboratories. The microphone consists of a 0.46-mmdiameter 2.25-µm-thick circular diaphragm and two circular backplates. The diaphragm is separated from each backplate by a 2-µm air gap. Experimental characterization of the microphone shows a sensitivity of 390 µV/Pa. The dynamic range of the microphone interfaced √ with a charge amplifier extends from the noise floor of 41 dB/ Hz up to 164 dB and the resonant frequency is 178 kHz. [2006-0190] Index Terms—Capacitive transducers, microphones, silicon micromachining.

I. I NTRODUCTION

I

N AN effort to reduce the impact of air travel on local communities surrounding airports, the Federal Aviation Administration (FAA) regulates the level of noise that aircraft may radiate [1]. Therefore, the aeroacoustic performance of an aircraft must be considered during its design. To design quieter aircraft, it is important to localize and quantify the sources of noise. The behavior of airframes and jet engines can be studied by conducting measurements on scale models in wind tunnels [2]. Aeroacoustic measurements are required to quantify the sound field and provide insight into the noise generation mechanisms so that the noise can be reduced to

Manuscript received September 3, 2006; revised August 19, 2007. This work was supported in part by the National Science Foundation under Grant ECS-0097636 and in part by the Sandia National Laboratories. Subject Editor K. Naiafi. D. T. Martin was with the Interdisciplinary Microsystems Group, Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611 USA. He is currently with Avago Technologies, Fort Collins, CO 80525-9790 USA (e-mail: [email protected]). J. Liu was with the Interdisciplinary Microsystems Group, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611 USA. He is currently with AdaptivEnergy LLC, Hampton, VA 23666 USA. K. Kadirvel is with the Interdisciplinary Microsystems Group, Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611 USA, and also with the Battery Monitoring Solutions Group, Texas Instruments, Melbourne, FL 32901 USA. R. M. Fox is with the Faculty of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611 USA. M. Sheplak is with the Interdisciplinary Microsystems Group, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611 USA. T. Nishida is with the Interdisciplinary Microsystems Group, Department of Electrical and Computer Engineering, and the Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611 USA. Digital Object Identifier 10.1109/JMEMS.2007.909234

acceptable levels. The microphone is a key component in an aeroacoustic measurement setup. The majority of microelectromechanical system (MEMS)based microphones are designed for audio applications, i.e., telephones and hearing aids [3]. The specifications for these applications include a bandwidth that is less than 20 kHz and a maximum pressure that is less than 120 dB (ref. to 20 µPa). Aeroacoustic microphones, however, have specifications that significantly differ from those of an audio microphone. The sound pressure level near a jet engine can be very high; therefore, an aeroacoustic microphone should be capable of distortion-free operation up to 160 dB. The FAA requires certification for commercial aircraft over the frequency range of 45 Hz < f ≤ 11.2 kHz [1]. However, aeroacoustic testing of aircraft and components is often conducted on scale models; therefore, the frequency range of interest is accordingly scaled up. For example, the frequency range for a one-eighth scale model extends up to 89.6 kHz. Thus, the bandwidth of an aeroacoustic microphone must extend up to 90 kHz to be capable of scale model testing [2]. If the microphone is too large, the interaction of the microphone with the sound field can cause diffraction at these high frequencies. This introduces errors in the frequency response [4]. If the sound field is known, these errors can be corrected. However, to avoid diffraction in general, the microphone size needs to be small compared to the acoustic wavelength [5]. Using a high-performance microphone enables accurate measurements and reproducible results. Some other microphone characteristics to consider are the dynamic range, sensitivity, bandwidth, stability, size, and cost [2]. The use of a MEMS technology for an aeroacoustic microphone offers several potential advantages. Microfabrication produces small diaphragm sizes that are desirable for aeroacoustic microphones. Furthermore, unlike small diaphragms made via traditional means, the MEMS diaphragms can be well controlled in terms of dimensions and stress [6]. Batch fabrication can be leveraged to produce microphones with closely matched specifications, which is beneficial for microphone arrays [7]. Additionally, the cost of a MEMS microphone has the potential to be lower than traditional microphones, provided there is sufficient volume [8]. The development of the MEMS microphone has been an active area of research over the past several decades [3]. These microphones have utilized many transduction schemes, including piezoresistive [9]–[12], piezoelectric [13]–[16], optical [17], [18], and capacitive [6], [19]–[22], [24]–[26]. Although successful microphones have been developed for each of these transduction schemes, capacitive microphones typically exhibit higher sensitivities and lower noise floors compared to the other

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TABLE I COMPARISON OF THE PREVIOUS AEROACOUSTIC MEMS MICROPHONES AND THE B&K 4138 TRADITIONAL CONDENSER MICROPHONE

types. In addition, piezoresistive microphones exhibit temperature drift and reduced performance at high temperatures due to junction leakage, increased thermodynamic noise, and lower π-coefficients [11]. There are several piezoelectric materials that can be used in piezoelectric microphones. Lead zirconate titanate is the most attractive material in terms of the dielectric and piezoelectric coefficients; however, it is incompatible with standard micromachining processes [16]. Optical microphones have the advantage that they can be deployed in harsh environments and are immune from electromagnetic interference; however, they require a stable light source and complex packaging [17], [18]. Several recent MEMS microphones have been designed for aeroacoustic applications. A single-backplate condenser microphone developed by Brüel and Kjær (B&K) demonstrated a linear response up to 140 dB and an A-weighted noise floor of 23 dB; however, its bandwidth was limited to 20 kHz [23]. This device has an octagon-shaped silicon nitride diaphragm with an effective radius of 1.95 mm. The microphone was packaged in a cartridge that is approximately the same size as a 1/4-in B&K microphone. A piezoresistive microphone has been reported that operates up to 160 dB, has √ a bandwidth up to 100 kHz, and has a noise floor of 52 dB/ Hz [11]. A piezoelectric microphone has been presented √ that has a linear response up to 169 dB, a noise floor of 48 dB/ Hz, and a 50-kHz bandwidth [16]. Finally, an optical microphone has been presented that had a theoretical bandwidth up to 100 kHz; however, its linear range √ was limited to 132 dB, and it had a high noise floor of 70 dB/ Hz [17]. Several other recent microphone designs have some specifications that are attractive for aeroacoustic applications. Hillenbrand and Sessler reported a piezoelectric microphone with a resonant frequency of approximately 140 kHz and a dynamic range of 37–164 dB [26]. Although this device has suitable performance, the diaphragm area of 0.3 cm2 is larger than desired for an aeroacoustic microphone. In addition, a capacitive microphone has a demonstrated bandwidth up to 50 kHz [24]; however, it has an insufficient dynamic range. Another capacitive microphone has been reported with a band-

width extending up to 100 kHz [25]; however, the upper limit of the dynamic range has not been reported. A comparison of these MEMS microphones to the conventional B&K 4138 1/8-in condenser microphone [23] is given in Table I. The piezoresistive [11] and the two piezoelectric microphones [16], [26] compare most favorably. Many of the listed MEMS microphones have significantly higher noise than the 4138. Although the capacitive microphone reported by Scheeper et al. [6] has a lower noise floor, it has a lower bandwidth, a lower maximum pressure, and a larger radius than the other MEMS microphones. There is opportunity for improvement by developing a capacitive MEMS microphone with a reduced noise floor while maintaining a high bandwidth and maximum pressure for aeroacoustic applications. The majority of the previous capacitive MEMS microphones are single-backplate condenser microphones. However, there has also been previous research into differential capacitive microphones. This type of microphone, described by Hunt [27], was first proposed for a MEMS microphone by Bernstein [28]. More recently, the differential capacitive MEMS microphone was discussed in greater detail [21], [29], [30]. These devices utilize a third electrode such that two capacitors exist, and there is a differential capacitance change due to an incident pressure. The use of a differential capacitive microphone has several advantages, including a potentially higher sensitivity due to the extra capacitor and a higher pull-in voltage enabling a higher sensitivity through the use of a higher bias voltage. Additionally, electrostatic force feedback can potentially be used to increase the bandwidth and linearity of the microphone [21], [29], [30]. A working dual-backplate capacitive microphone has been published; however, it was designed for audio applications [21]. It measures a maximum pressure of 118 dB and has a bandwidth of 20 kHz. This paper details the theory, fabrication, and characterization of a dual-backplate capacitive microphone for aeroacoustic measurements and extends preliminary results reported in past conference papers [31], [32]. The details of the microphone structure and operation are discussed in Section II. In

MARTIN et al.: DUAL-BACKPLATE CAPACITIVE MICROPHONE FOR AEROACOUSTIC MEASUREMENTS

Fig. 1.

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Schematic of the dual-backplate microphone showing key layers and features (not to scale). (a) Schematic top view. (b) Schematic cross-sectional view.

Section III, the fabrication of the microphone is presented. Experimental results for the fabricated microphone are given in Section IV, as well as a comparison of this device to previous aeroacoustic microphones. II. M ODELING AND D ESIGN In this section, the dual-backplate microphone structure is introduced and its theory of operation is discussed. This is followed by the development of a lumped element model, microphone design, and modeling of the frequency response and noise floor. A. Device Structure The dual-backplate microphone structure is shown in Fig. 1. The microphone consists of three parallel circular plates: 1) the diaphragm; 2) top backplate; and 3) bottom backplate. The diaphragm is located between the two backplates, which are perforated with holes. The backplate holes allow the incident pressure to deflect the diaphragm and reduce damping in the air gaps. There is a large cavity beneath the microphone structure to minimize sensitivity loss due to cavity stiffening. Both of the backplates and the diaphragm are made of phosphorous-doped polysilicon and create two capacitors. Capacitor C1 is comprised of the top backplate and the diaphragm, and C2 is comprised of the bottom backplate and the diaphragm. The capacitance values change due to diaphragm deflection, which can be detected by various types of interface electronics.

As shown in Fig. 1(b), the microphone essentially consists of three concentric shells. The top backplate, diaphragm, and bottom backplate all anchor down to the substrate. The anchors in Fig. 1(b) are not drawn to scale. The anchor for the diaphragm is approximately 20 µm wide, whereas the diaphragm thickness is 2.25 µm, as depicted in Fig. 2(a). As a result of this anchor geometry, the three plates of the microphone have slightly different radii. Electrical connections to the diaphragm and bottom backplate are routed through openings in the anchor for the top backplate and diaphragm, respectively. The connection for the bottom backplate is shown in Fig. 2(b). The air channel created between the poly0 layer and the diaphragm and top backplate anchors prevents short circuits between the three microphone plates. This channel also serves as the pressure equalization vent when the back cavity is sealed. B. Diaphragm Model To find the change in capacitance due to an incident pressure, the diaphragm deflection must first be determined. The diaphragm is assumed to be homogeneous, axisymmetric, and linearly elastic. Furthermore, the diaphragm is assumed to have a perfectly clamped boundary condition around the perimeter of the diaphragm and to have zero residual in-plane stress. Assuming small deflection theory, the transverse deflection of the diaphragm is [33] w(r) =

r 2 2 −pd a4 1− 64D a

(1)

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Fig. 3. Schematic of a dual-backplate capacitive microphone biased with two voltage sources of equal magnitude and opposite polarity.

Fig. 2. Schematics showing details of the microphone anchor structure and electrical connections. (a) Schematic cross section showing anchor details. (b) Schematic cross section showing details of electrical connections to inner plates (poly0 3× actual thickness).

where the center deflection of the plate is w(0) =

−pd a4 64D

(2)

and pd is the pressure acting on the diaphragm, a is the radius of the diaphragm, D is the flexural rigidity, and r is the radial coordinate. As long as the center deflection of the diaphragm is small compared to the diaphragm thickness, (1) is valid. As the diaphragm deflection becomes larger, the internal strain of the plate cannot be neglected. The internal strain reduces the deflection for large displacements. An analytic approximation for the large deflection behavior is [33] 1 −pd a4 wNL (0) = 2 . 64D 1 + 0.488 w(0) 2

Fig. 4. Schematic of a dual-backplate capacitive microphone with a charge amplifier.

The capacitors of the microphone are modeled as parallel plate capacitors with a capacitance of C = 0 A/g. As the diaphragm deflects due to an incident pressure, the capacitance of C1 and C2 change. The bias voltages force a charge on the capacitors given by Q = CV . For small deflections, the change in the charge on the top and bottom capacitors is

(3)

h

The deflection predicted by this model is very close to that predicted by finite element analysis, as well as an exact analytical model that is valid for diaphragms with in-plane stress [34]. The transition between linear and nonlinear behavior as a function of pressure is captured by (2) and (3). C. Electrical Model In this section, the electrostatic behavior of a dual-backplate capacitive microphone assuming constant voltage bias across the two capacitors is discussed. A schematic of the dual-backplate microphone biased with constant voltages is shown in Fig. 3. The top backplate is biased with a voltage VB , and the bottom backplate is biased with a voltage of −VB . Both backplates are initially a distance g0 from the diaphragm, which moves a distance g due to a pressure pd acting on the diaphragm. A positive pd moves the diaphragm closer to the bottom backplate. This results in a negative g for the top capacitor and a positive g for the bottom capacitor.

∆Q1 =

g 1 VB C10 3 g0

(4)

∆Q2 =

g 1 VB C20 3 g0

(5)

and

where C10 and C20 are the nominal capacitance of the top and bottom capacitors, 0 is the permittivity of free space, g0 is the nominal gap distance, and g is the change in the gap distance. The 1/3 factor accounts for the effective area of the diaphragm. To find the output voltage, the microphone is considered with a charge amplifier, as shown in Fig. 4. The amplifier consists of an operational amplifier with a feedback capacitor Cfb ; the bias details are not shown for clarity. The input charge to the amplifier Qin is stored on Cfb , resulting in the output voltage. The input to the amplifier is held at small-signal ground; thus, the voltage on the parasitic capacitor Cp is constant. Therefore, the parasitic capacitance does not affect the sensitivity of the capacitive microphone buffered with a charge amplifier. The input charge to the amplifier Qin is the sum of ∆Q1 and ∆Q2 . The charge amplifier stores the input charge Qin on the


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feedback capacitor to generate an output voltage equal to Vout =

−Qin . Cfb

(6)

Neglecting the different areas of the three plates, the total input charge is twice that of a comparable single-backplate capacitive microphone. Furthermore, the output voltage Vout = −

2 VB C10 g 3 g0 Cfb

(7)

is also twice that of a single-backplate capacitive microphone, assuming C10 = C20 and ∆C10 = ∆C20 . By substituting the diaphragm deflection given by (2) for g , the final expression for the output voltage of a dual-backplate capacitive microphone is Vout =

2 VB C10 a4 pd . 3 g0 Cfb 64D

(8)

In Section II-D, the pressure acting on the diaphragm pd will be related to the incident pressure. The voltage between the plates of the microphone creates an electrostatic force that acts on the diaphragm. This force opposes the mechanical restoring force of the diaphragm. This force is nonlinear, quadratically increasing as the diaphragm approaches a backplate, and causes an instability in the microphone [8]. In equilibrium, the total force acting on the diaphragm is Fnet = 2VB2

0 Ag0 g g − = 0, 2 2 2 (g0 − g ) Cm,d

(9)

where VB is the bias voltage, g0 is the nominal gap distance, and g is the diaphragm deflection. While at rest, the microphone is stable as long as the bias voltage is less than a critical pull-in voltage. The pull-in voltage for a dual-backplate microphone is g0 3 , (10) VPI = 2Cm,d 0 A where Cm,d is the mechanical compliance of the diaphragm. The lumped elements of the microphone are further discussed in Section II-D. This result agrees with previous results stating that the pull-in voltage for a dual-backplate microphone is approximately 30% higher than that of a corresponding singlebackplate microphone [21], [30]. D. LEM The acoustic properties of the microphone structure are modeled using lumped element modeling (LEM), in which the distributed properties of the microphone are represented by set of lumped elements [35]. This modeling technique is valid as long as the microphone is small compared to the acoustic wavelength. The microphone structure is modeled in the acoustic energy domain. The acoustic domain is coupled to the electrical domain through ideal transformers [8]. A simplified electroacoustic lumped element model of the microphone is shown in Fig. 5. The acoustic behavior of

Fig. 5. Simplified electroacoustic lumped element model of the dualbackplate microphone.

the microphone is modeled to predict diaphragm deflection as a function of incident pressure. The incident pressure pin passes through the microphone and creates a pressure pd that deflects the diaphragm. This pressure then causes an output voltage via the two moveable capacitors, as modeled by two transformers. The acoustic compliance of the top backplate, diaphragm, and bottom backplate are represented by Ca,bp1 , Ca,d , and Ca,bp2 , respectively. The acoustic resistance of the top and bottom backplate holes are represented by Ra,bp1 and Ra,bp2 , respectively. Ra,v represents an acoustic vent resistance from the cavity to the incident acoustic field. Finally, Ca,cav is the acoustic compliance of the cavity. Several elements of the microphone structure are neglected in this model. The acoustic compliance of the cavities between the diaphragm and each backplate is much smaller than the large cavity; thus, they are not included in the model. Furthermore, the mass of the backplates is neglected because the microphone is operated in a compliant mode, and the resonance is dominated by the diaphragm mass. The structural damping of the diaphragm is neglected because it is typically much less than the backplate resistances. The vent channel is significant only at low frequencies; therefore, the acoustic mass of the vent channel is neglected. The transduction from the acoustic domain to the electrical domain is represented by two transformers. A pressure acting on the diaphragm results in a voltage for the top and bottom capacitors that are represented by vo1 and vo2 , respectively. The microphone output is either a charge or a voltage, depending on the type of interface circuit that is used. When used with a charge amplifier, the diaphragm voltage is held fixed, and the output of the microphone is a charge. The turns ratios for the transformers n1 and n2 determine the output charge for a given pressure. The two capacitors of the microphone are modeled by Ce,10 and Ce,20 . The acoustic compliance of a circular plate Ca,p =

πa6 (1 − ν 2 ) 16Eh3

(11)

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represents the storage of potential energy as the plate deflects. The storage of kinetic energy is modeled by the lumped acoustic mass of the circular plate Ma,p =

9ρh , 5πa2

(12)

where ρ is the density of the plate material. This model of the plate is valid up to the first resonant frequency [35]. The backplate resistances Ra,bp represent the losses due to the air gap and the acoustic holes. It is comprised of the sum of two components: 1) Ra,g and 2) Ra,h , which represent losses in the air gap and backplate holes, respectively. The first component of the resistance, which is known as squeeze-film damping, is given by [36] Ra,g =

12µair B(Ar ), πnh g03

(13)

where µair is the viscosity of air, nh is the number of backplate holes, and g0 is the nominal air gap. The term Ar is the ratio of the total area of the backplate holes to the area of the backplate, and B(Ar ) is defined as 1 1 1 3 1 B(Ar ) = ln (14) − + Ar − A2r . 4 Ar 8 2 8

Fig. 6. Transformer modeling the transduction from the acoustic domain to the electrical domain of one capacitor.

this approximates the condition when the microphone is connected to a charge amplifier. The pressure across the diaphragm compliance pd results in a voltage vo1 through the transformer. This voltage is given by vo1 = n1 pd . To complete the lumped element model shown in Fig. 5, the turns ratios n1 and n2 must be determined. The pressure pd results in a deflection of the diaphragm g , which is approximated by (2). This results in a change in the charge on the top and bottom microphone capacitors, as given by (4) and (5), respectively. Thus, (4) and (5) can be written as

72µair hbp , πa4h nh

(15)

where ah is the radius of each backplate hole, and hbp is the thickness of the backplate. The storage of potential energy in the compressed air in the cavity is represented by an acoustic compliance given by Ca,cav =

Vcav , ρair c2

(16)

where the volume of the cavity is given by Vcav , and c is the isentropic speed of sound. This model is valid for kL < 0.3, where L is the depth of the cavity [4]. The final acoustic element to be considered is the effect of the vent channel. Modeling the flow in the channel as fully developed laminar flow, the acoustic resistance in the channel is [38] Ra,v =

128µLeff πD4

(17)

where Leff is the effective length of the channel, and D is the hydraulic diameter. The transduction portion of the lumped element model is constructed by considering the relationship between a pressure acting on the diaphragm and the output charge. The timevarying small-signal pressure on the diaphragm changes the capacitance of both the top and bottom capacitors, resulting in two components to the output charge. A model of one of the transformers is shown in Fig. 6. The output is grounded, as

−pd C10 VB a4 3 g0 64D

(18)

∆Q2 =

−pd C20 VB a4 . 3 g0 64D

(19)

and

The second component of the backplate resistance, which is due to losses in the backplate holes, is [37] Ra,h =

∆Q1 =

In the circuit shown in Fig. 6, the change in charge on the capacitor is given by ∆Q1 = Ce,10 vo1 , which can be rewritten as ∆Q1 = Ce,10 n1 pd . Similarly, the change in charge on capacitor C2 is ∆Q2 = Ce,20 n2 pd . Therefore, n1 and n2 are given by n1 = −

1 VB a4 3 g0 64D

(20)

n2 = −

1 VB a4 3 g0 64D

(21)

and

respectively. The dual-backplate transformer model considers the geometry of each capacitor. As seen from (18) and (19), the output charge depends on the nominal capacitance value of each capacitor. Therefore, this model considers the effect if the areas of the two capacitors are not matched. It is also noted that the turns ratios for the transformers are not directly related to the two device capacitances. Rather, the turns ratios are a function of the nominal gap distance g0 and the diaphragm geometry. E. Microphone Design The dual-backplate microphone was designed to have a linear response up to a maximum pressure of 160 dB and a bandwidth of at least 100 kHz. The microphone structure, as depicted in Figs. 1 and 2, was designed for fabrication using the SUMMiT V process at Sandia National Laboratories. In this


TABLE II MICROPHONE PHYSICAL PROPERTIES

process, the thickness of each layer is fixed, and the in-plane stress of each polysilicon layer is approximately zero [39]. The use of the SUMMiT V process has several advantages and disadvantages for this microphone. The low-stress phosphorous-doped polysilicon is advantageous for constructing a conducting compliant diaphragm. However, the polysilicon layers also result in compliant backplates. The microphone must be designed such that the compliant backplates will not cause operational problems. The flat structural layers and the use of chemical mechanical polishing result in a uniform gap between the diaphragm and each backplate. Furthermore, the use of the SUMMiT V process imposes constraints on the thickness and material properties of each of the three plates of the microphone. As a result, the only design variables were the diaphragm radius and the backplate hole geometry. Therefore, the microphone geometry is overconstrained, and an optimal design is not possible. The microphone dimensions and material properties [39] are summarized in Table II. The dimensions of the backplates are similar to those of the diaphragm. As a result, the compliance of the three plates is similar. The backplate holes are designed such that the backplate deflection is negligible for the frequencies of interest. The backplate resistance and compliance have a first-order time constant and corresponding corner frequency, below which the backplate deflection is negligible. For this microphone, the corner frequencies are 1.3 and 3.3 MHz for the top and bottom backplates, respectively. Other considerations for the backplate design include providing sufficient holes for the release etch and preventing the microphone from being overdamped. The diaphragm radius was chosen to maximize the diaphragm compliance while providing linear operation up to 160 dB. Specifically, the diaphragm was designed such that the difference between the ideal linear deflection and the physical nonlinear deflection is 3%. The values of the lumped elements for the designed microphone are given in Table III. The theoretical frequency response of the microphone is plotted in Fig. 7, as predicted by the

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TABLE III ACOUSTIC LUMPED ELEMENT VALUES FOR THE DESIGNED MICROPHONE

Fig. 7. Theoretical frequency response of the microphone predicted by LEM. (a) Theoretical magnitude response. (b) Theoretical phase response.

lumped element model. The predicted resonant frequency of the microphone is approximately 170 kHz. F. Noise Model The minimum detectable signal of the microphone is determined by noise sources from both the microphone and interface circuitry. As was shown in Fig. 4, the dual-backplate microphone was packaged with a charge amplifier. The TLE2071 operational amplifier manufactured by Texas Instruments was used to construct the charge amplifier. The noise analysis is broken into two parts. First, the acoustic noise sources within the microphone are considered. Then, the electrical noise sources from the interface electronics are analyzed. The acoustic noise is referred to the electrical domain through the equivalent circuit model.

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Fig. 8. Acoustic noise model of the microphone. Fig. 10. Theoretical noise of the microphone and charge amplifier showing the contributions from each noise source.

Fig. 9. Noise model of the charge amplifier coupled to the microphone.

A simplified lumped element model of the dual-backplate microphone, including noise sources, is shown in Fig. 8. In this model, the backplate compliances have been neglected because they are insignificant for the designed microphone. Furthermore, the backplate damping and internal structural damping of the diaphragm have been combined into a single equivalent acoustic resistor Reff with an associated noise source. To find the noise contributions of the acoustic damping within the microphone, the noise from each of the sources is referred to the port labeled pd . Each resistor in Fig. 8 has a thermomechanical noise source, which can be represented by either a volume velocity noise or a pressure noise. The power spectral density (PSD) of these sources is 4kT /Ra and 4kT Ra , respectively [40]. These two noise sources are shaped by the dynamics of the microphone, which are represented by the LEM. The noise due to Ra,eff is flat between the cut-on frequency and resonant frequency of the microphone. However, the noise PSD due to the vent resistor is proportional to 1/f 2 in the same frequency range. Thus, the vent resistor is the dominant acoustic noise source for low frequencies. The charge amplifier and associated noise sources are shown in Fig. 9. The pressure noise due to Ra,eff and Ra,v couples to the electrical domain through the transformers. In addition, the feedback resistor and amplifier both contribute electrical noise. The noise from the feedback resistor is modeled as a current with a PSD of 4kT /Re . The current noise from Rfb and the amplifier are shaped by the feedback impedance. The amplifier

voltage noise is scaled by the ratio of the feedback impedance to the input impedance. Thus, the parasitic capacitance increases the contribution of the amplifier’s input referred voltage noise to the total output noise. The value of the feedback resistor is 2 GΩ. The feedback capacitor has a net value of 1.5 pF. The net parasitic capacitance is represented by Cp . This is estimated to be approximately 20 pF, including the cable capacitance, parasitic capacitance on the PCB, and the amplifier input capacitance. The output PSD of these electrical noise sources, as well as the total contribution from the acoustic damping, is plotted in Fig. 10. It is apparent that the electrical noise dominates the overall noise floor of the system. Below 2 kHz, the current noise from the amplifier and feedback resistor dominates. Above this frequency, the amplifier voltage noise is most significant. The noise is also shaped by the cut-on frequency of the charge amplifier, which is 53 Hz. III. F ABRICATION Fabrication of the microphone begins with the SUMMiT V process [39]. Cross sections of the key SUMMiT V microphone fabrication steps are shown in Fig. 11(a). The process begins with a 650-µm-thick silicon wafer and growth of a 0.6-µmthick layer of thermal oxide. This is followed by the deposition of 0.8 µm of silicon nitride, as shown in step 1. The first polysilicon layer, i.e., poly0, is deposited and patterned to form electrical interconnections and anchors for the structural layers. Next, the first layer of sacrificial oxide is deposited and patterned to open anchor holes. The two polysilicon layers, which are poly1 and poly2, are combined to form the bottom backplate resulting in a 2.5-µm-thick polysilicon layer, as shown in step 2. In step 3, another layer of sacrificial oxide is then deposited and patterned. This 2-µm-thick oxide layer defines the gap between the bottom backplate and diaphragm. The diaphragm is formed from poly3, which is a 2.25-µm-thick layer of polysilicon. In step 4, a 2-µm layer of sacrificial oxide is deposited which determines the gap distance between the diaphragm and top backplate. The final layer 2.25 µm layer of polysilicon, i.e., poly4, is deposited and patterned to form the top backplate. After the completion of the SUMMiT V process, the postprocessing is carried out at the University of Florida,


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Fig. 11. Process flow for the fabrication of the dual-backplate capacitive microphone (not to scale). (a) SUMMiT V process. (b) Postprocessing.

Fig. 12. Close-up view of the microphone structure and wirebond connections.

Gainesville, FL on individual die. Cross sections of the postprocessing are shown in Fig. 11(b). The first step of the postprocess, i.e., step 5, is a backside through-wafer deep reactive ion etching (DRIE). This creates the cavity below the diaphragm. Next, the thin layers of silicon dioxide and silicon nitride are removed in step 6. The final step is the removal of the sacrificial oxide. The oxide is removed in a liquid 49% hydrofluoric acid etch. A supercritical CO2 release is used to avoid stiction [41]. The cross section of the finished microphone is schematically shown in step 7 of the process flow. The fabricated microphone is shown in Fig. 12. This image shows the microphone after it has been released and packaged. The structure of the fabricated microphone is shown in Fig. 13. These images are from a sectioned unreleased die. A focused ion beam is used to smooth the surfaces. The cross section shown in Fig. 13(a) shows the three layers of the microphone as well as top and bottom backplate holes.

Fig. 13. SEM images of an unreleased microphone showing a cross-sectional view of several locations of the microphone. (a) SEM image showing a cross section of the microphone. (b) SEM image of the electrical connection to the diaphragm.

The cross section shown in Fig. 13(b) shows the details of the electrical connection to the diaphragm. Here, the anchor for the top backplate does not extend down to the substrate. A polysilicon layer, i.e., poly0, runs underneath the top backplate

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Fig. 16. Experimental setup to determine the resonant frequency of the microphone.

Fig. 14. Schematic of the microphone package.

Fig. 15. Experimental setup for acoustic characterization in a PWT.

anchor to connect the diaphragm anchor to a polysilicon line outside of the microphone structure. IV. R ESULTS AND D ISCUSSION The dual-backplate capacitive microphone was characterized in terms of its linearity, frequency response, noise floor, and dynamic range. First, the experimental setup is presented, then the experimental results are discussed. A. Experimental Setup The microphone packaging was designed for laboratory experimentation. Specifically, it was designed such that the microphone would be flush mounted for the acoustic measurements, as shown in Fig. 14. The microphone is affixed into a recess in a printed circuit board (PCB). Wire bonds are made from the microphone to gold pads on the PCB. The PCB is then embedded in a lucite block. The front of the package has an area of 0.75 × 0.75 in. Symmetric bias voltages of ±9.3 V were used for the characterization. The microphone was acoustically characterized in terms of its frequency response and linearity. An acoustic waveguide, or plane wave tube (PWT), was used for these experiments, as shown in Fig. 15 [44]. A PWT is a rigid-walled duct that only supports the propagation of acoustic plane waves below a cutoff frequency. The value of the cutoff frequency depends on the geometry of the PWT [4]. The device under test and a

reference microphone are both placed at the end of the tube. The tube is filled with helium to extend the range of operation to approximately 20 kHz. Key elements in the acoustic setup include a BMS 4590P compression driver and a B&K Pulse Multi-analyzer system. A B&K 4138 condenser microphone was used for the reference for the frequency response measurement. A PCB 377A51 condenser microphone is the reference for the linearity measurement. The pulse system is used to generate the signal for the acoustic driver, receive the inputs from the two microphones, and perform the data analysis. For the linearity measurement, a single tone pressure was applied at 1 kHz; a bin width of 4 Hz was used with 50 averages. A periodic random signal over the range of 300 Hz–25.4 kHz was applied for the frequency response measurement. Data above 20 kHz were discarded because higher order modes propagate at these frequencies. The bin width was 16 Hz with 500 averages for the frequency response measurement. The resonant frequency of the microphone was determined using a Polytec Scanning Doppler Laser Vibrometer. The microphone is placed on the stage of a microscope. A Polytec OFV 511 fiber interferometer generates a laser beam that is directed through the microscope, through the center hole of the top backplate, and is incident on the microphone diaphragm, as shown in Fig. 16. The fiber interferometer also receives the reflected optical signal through the microscope adapter. The velocity is inferred from the returned optical signal by the vibrometer controller [42]. A Stanford Research Systems DS345 function generator is connected to the microphone to apply a square wave between the diaphragm and top backplate. The electrostatic force actuates the diaphragm. The velocity of the diaphragm is numerically integrated, resulting in a time series of the displacement step response [42]. The noise measurements were conducted in a Faraday cage. The Faraday cage was used to minimize electromagnetic interference, in particular 60-Hz powerline interference and harmonics. The microphone and DN620 charge amplifier were placed inside the Faraday cage. The output was connected to a Stanford Research Systems SR785 dynamic signal analyzer that measured the output PSD of the amplifier. The noise spectrum was measured from 10 Hz to 102.4 kHz over three ranges. The first ranged from 10 to 200 Hz with a bin width of 0.25 Hz and 2300 averages. The second range spanned from 200 Hz to 1.6 kHz and had a bin width of 2 Hz and 4000 averages.


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Fig. 17. Sensitivity of the microphone at 1 kHz for varying amplitudes.

The final frequency range spanned from 1.6 to 102.4 kHz with a 128-Hz bin width and 30 000 averages [43]. B. Characterization In this section, the experimental results are discussed. The microphone was characterized in terms of its frequency response, dynamic range, linearity, and resonant frequency. The linearity of the microphone was characterized in the PWT experimental setup described in Section IV-A. The acoustic driver produced a 1-kHz sinusoidal pressure input. The amplitude of the pressure was varied from a sound pressure level of 80 to 164 dB. At each sound pressure level, the sensitivity of the microphone was recorded. The response of the microphone to the applied pressure is shown in Fig. 17. The microphone exhibits a linear response up to 164 dB, which is the limit of the acoustic driver, with a deviation of +0.7 dB. The measured sensitivity at 1 kHz is 390 µV/Pa. The frequency response was measured over the range of 300 Hz–20 kHz. An overall flat response was measured over this range, as shown in Fig. 18(a). There is some ripple evident in the magnitude and phase response [Fig. 18(b)]. This is caused by coupling of vibration in the package mounting and cabling to a signal in the microphone output voltage. Securing the cable from the microphone to the amplifier reduced the amount of ripple. Although the highest frequency tested was 20 kHz, the frequency response should remain flat up to near the resonant frequency of 178 kHz. The resonant frequency of the microphone was found by measuring the step response of the diaphragm using a scanning laser vibrometer. The data are fit to the predicted diaphragm response due to a voltage step, giving an estimate for the resonant frequency of 178 kHz. The measured displacement data and the curve-fitting result are shown in Fig. 19. The noise floor of the microphone and charge amplifier was measured in the Faraday cage. A bias was applied to both the microphone and amplifier. The output PSD of the amplifier was measured without any acoustic excitation. The measured output PSD is compared to the theoretical noise in Fig. 20, over the range from 10 Hz to 102.4 kHz. The setup noise was subtracted from the measured noise. As can be seen in Fig. 20, the setup noise is well below the value of the measured noise and, therefore, does not impact

Fig. 18. Frequency response of the microphone up to 20 kHz. (a) Experimental magnitude response. (b) Experimental phase response.

Fig. 19. Time series data of the diaphragm step response.

the measurement. Below 10 kHz, the noise floor is dominated by the current noise of the feedback resistor and amplifier. At 1 kHz, the output PSD has a value of 8.0 × 10−13 V2 /Hz. Dividing by the measured sensitivity of 390 µV/Pa √yields a corresponding input referred noise level of 41 dB/ Hz for the TLE2071-based charge amplifier. Martin √ et al. previously reported an incorrect noise figure of 42 dB/ Hz for the DN620 charge √ amplifier, these data should have been reported as 58 dB/ Hz [31], [32]. The measured noise is higher than the predicted noise. The mismatch between the model is most likely due to uncertainties in the amplifier noise model and underestimating the parasitic

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There are several tradeoffs for the choice of interface circuitry to be used with the microphone. The microphone possesses a capacitance less than 1 pF. Furthermore, the SUMMiT V process does not allow circuitry to be integrated with the microphone on-chip. Therefore, a hybrid package is needed in which the microphone die and amplifier die are packaged together. A charge amplifier was used for the preliminary characterization to minimize sensitivity losses due to parasitic capacitances. However, the use of a charge amplifier results in excessive noise, compared to a voltage amplifier. In the future, the microphone will be packaged with a voltage amplifier with a low input capacitance. Reduced electrical noise is expected at the cost of a lower sensitivity due to the parasitic capacitance. Fig. 20. Output PSD noise of the microphone and charge amplifier. Theoretical noise and setup noise of the spectrum analyzer are also shown.

V. C ONCLUSION TABLE IV SUMMARY OF THE MEASURED RESULTS OF THE MICROPHONE

capacitance. Increased parasitic capacitance raises the noise level, particularly at higher frequencies.

C. Discussion The performance of the dual-backplate microphone is summarized in Table IV. There are some differences between the measured results and the theoretical performance. This is most likely due to process variations that could result in a stiffer diaphragm. The most variable parameter in the SUMMiT V process is the thickness of the sacrificial oxide layers. This directly affects the microphone air gap distances. The dual-backplate microphone favorably compares with the MEMS aeroacoustic microphones listed in Table I. This device has a smaller radius than the other aeroacoustic MEMS microphones. This limits scattering errors at high frequencies. Two of the previous microphones measure sound pressure levels up to 160 dB [11], [16]; however, the dual-backplate capacitive microphone has a lower noise floor than these two microphones. The single-backplate microphone has the lowest noise floor of the selected aeroacoustic microphones; however, it has a dynamic range that is limited to 141 dB and bandwidth that is limited to 20 kHz [6].

A dual-backplate capacitive microphone has been designed for aeroacoustic applications. The microphone was fabricated using both the SUMMiT V process at Sandia National Laboratories as well as facilities at the University of Florida. The fabrication process utilized both surface and bulk micromachining, including the use of a DRIE and supercritical CO2 drying. Device characterization shows that the microphone meets the design goals and favorably compares to the previous MEMS aeroacoustic microphones. The device has a sensitivity of 390 µV/Pa,√a resonant frequency of 178 kHz, and a noise floor of 41 dB/ Hz. The dynamic range extends up to 164 dB. This paper demonstrates the first dual-backplate capacitive microphone designed for aeroacoustic measurements. Future work includes testing the microphones in a high-frequency free field calibration test setup that is currently under development. Furthermore, a low-noise voltage amplifier will be utilized to further reduce the noise floor of the system. ACKNOWLEDGMENT The authors would like to thank A. Ogden from the University of Florida Nanofabrication Facilities for assistance with the packaging of the microphone; S. Tedeschi, who is a graduate student in the Department of Materials Science and Engineering, University of Florida, for preparing the SEM images of the microphone; Prof. H. Chan of the Department of Physics, University of Florida for assistance with the supercritical CO2 release; and the reviewers for their detailed suggestions that have significantly improved the presentation and clarity of this paper. R EFERENCES [1] “Aeronautics and space, noise standards: Aircraft type and airworthiness certification,” Title 14 US Code of Federal Regulations, pt. 36, 2004. [2] T. J. Mueller, Aeroacoustic Measurements. Berlin, Germany: SpringerVerlag, 2002, pp. 158–179. [3] P. R. Scheeper, A. G. H. van der Donk, W. Olthuis, and P. Bergveld, “A review of silicon microphones,” Sens. Actuators A, Phys., vol. 44, no. 1, pp. 1–11, Jul. 1994. [4] D. T. Blackstock, Fundamentals of Physical Acoustics. Hoboken, NJ: Wiley, 2000. [5] J. Eargle, The Microphone Handbook. London, U.K.: ButterworthHeinemann, 2001. [6] P. R. Scheeper, B. Nordstrand, B. L. J. O. Gullov, T. Clausen, L. Midjord, and T. Storgaard-Larsen, “A new measurement microphone based on


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[32] D. T. Martin, J. Liu, K. Kadirvel, R. M. Fox, M. Sheplak, and T. Nishida, “Development of a MEMS dual backplate capacitive microphone for aeroacoustic measurements,” presented at the 44th AIAA Aerospace Sciences Meeting Exhibit, Reno, NV, 2006, AIAA Paper #2006-1246. [33] S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells. New York: McGraw-Hill, 1959. [34] M. Sheplak and J. Dugundji, “Large deflections of clamped circular plates under tension and transitions to membrane behavior,” J. Appl. Mech., vol. 65, no. 1, pp. 107–115, 1998. [35] M. Rossi, Acoustics and Electroacoustics. Norwood, MA: Artech House, 1988, ch. 5/6. [36] Z. Skvor, “On the acoustical resistance to viscous losses in the air gap of electrostatic transducers,” Acoustica, vol. 19, pp. 295–299, 1967. [37] D. Homentcovschi and R. N. Miles, “Modeling of viscous damping of perforated planar microstructures. Applications in acoustics,” J. Acoust. Soc. Amer., vol. 116, no. 5, pp. 2939–2947, Nov. 2004. [38] R. W. Fox, A. T. McDonald, and P. J. Pritchard, Introduction to Fluid Mechanics, 6th ed. New York: Wiley, 2004, ch. 8. [39] J. J. Sniegowski and M. S. Rodgers, “Multi-layer enhancement to polysilicon surface-micromachining technology,” in Proc. IEDM Tech. Dig., 1997, pp. 903–906. [40] T. B. Gabrielson, “Mechanical-thermal noise in micromachined acoustic and vibration sensors,” IEEE Trans. Electron Devices, vol. 40, no. 5, pp. 903–909, May 1993. [41] G. T. Mulhern, D. S. Soane, and R. T. Howe, “Supercritical carbon dioxide drying of microstructures,” in Proc. Int. Conf. Solid-State Sens. Actuators, 1993, pp. 296–299. [42] J. Liu, D. Martin, K. Kadirvel, T. Nishida, L. Cattafesta, M. Sheplak, and B. P. Mann, “Nonlinear model and system identification of a capacitive dual-backplate MEMS microphone,” J. Sound Vib., vol. 309, pp. 276–292. [43] R. Dieme, G. Bosman, M. Sheplak, and T. Nishida, “Source of excess noise in silicon piezoresistive microphones,” J. Acoust. Soc. Amer., vol. 119, no. 5, pp. 2710–2720, May 2006. [44] T. Schultz, L. Cattafesta, and M. Sheplak, “Modal decomposition method for acoustic impedance testing square ducts,” J. Acoust. Soc. Amer., vol. 120, no. 6, pp. 3750–3758, Dec. 2006.

David T. Martin received the B.S. degree in electrical engineering and the M.S. and Ph.D. degrees in electrical and computer engineering from the University of Florida, Gainesville, in 2001, 2005, and 2007, respectively. His Ph.D. research was conducted as part of the work of the Interdisciplinary Microsystems Group and was focused on the development of a MEMS dual-backplate capacitive microphone. He is currently with Avago Technologies, Fort Collins, CO, working on process integration for MEMS transducers. His research interests include MEMS transducers, acoustic modeling, and MEMS packaging.

Jian Liu was born in Boyang, China, in 1977. He received the B.E. and M.S. degrees from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1998 and 2001, respectively, and the M.S. and Ph.D. degrees from the University of Florida, Gainesville, in 2003 and 2006, respectively. His Ph.D. dissertation was the study of nonlinear dynamics of a dual-backplate capacitive MEMS microphone. From 1998 to 2001, he worked on the design, modeling, simulation and characterization of a linear piezoelectric ultrasonic motor. Since 2006, he has been a Key Mechanical Analyst with AdaptivEnergy LLC, Hampton, VA, working on the research and development of piezo-based actuators and energy harvesters. Dr. Liu is a member of the American Institute of Aeronautics and Astronautics and the American Society of Mechanical Engineers.

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Karthik Kadirvel received the B.Eng. (gold medalist) degree in electronics and instrumentation from Annamalai University, Tamil Nadu, India, in May 2000 and the M.Sc. degree from the University of Florida, Gainesville, in December 2002. He is currently working toward the Ph.D. degree in the design of interface circuits for MEMS capacitive transducers with the Interdisciplinary Microsystems Group, Department of Electrical and Computer Engineering, University of Florida. In the summer and fall of 2005, he was a Graduate Technical Intern with the Flash Memory Group, Intel Corporation, Folsom, CA. He is concurrently an Intern with the Battery Monitoring Solutions Group, Texas Instruments, Melbourne, FL, working on the design of mixed-signal integrated circuits. Mr. Kadirvel received a Predoctoral Fellowship Award from Texas Instruments in 2003.

Mark Sheplak received the B.S., M.S., and Ph.D. degrees in mechanical engineering from Syracuse University, Syracuse, NY, in 1989, 1992, and 1995, respectively. From 1992 to 1995, he was a GSRP Fellow with the NASA-Langley Research Center, Hampton, VA. From 1995 to 1998, he was a Postdoctoral Associate with the Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge. Since 1998, he has been with the University of Florida, Gainesville, where he is currently an Associate Professor with the Interdisciplinary Microsystems Group, Department of Aerospace and Mechanical Engineering and an Affiliate Associate Professor of electrical and computer engineering. His current research interests include the design, fabrication, and characterization of high-performance instrumentationgrade MEMS-based sensors and actuators that enable the measurement, modeling, and control of various physical properties.

Robert M. Fox received the B.S. degree in physics from the University of Notre Dame, Notre Dame, IN, in 1972 and the M.S. and Ph.D. degrees in electrical engineering from Auburn University, Auburn, AL, in 1981 and 1986, respectively. Since 1986, he has been with the Faculty of Electrical and Computer Engineering, University of Florida, Gainesville, where he is currently an Associate Professor and Associate Department Chair. His research interests are circuit design and modeling for advanced IC technologies and design-oriented analysis of analog integrated circuits, including low-voltage circuit techniques and analog and RF test strategies. He has worked on a variety of topics, including analog circuit designs, cryogenic electronics, circuit designs with SOI, radiation response of semiconductors, noise modeling, and modeling of transistor self heating. Dr. Fox is a member and the former Chair of the Analog Signal Processing Technical Committee of the IEEE Circuits and System Society. He is a member and the former Chair of the Analog/Digital Circuits Technical Subcommittee for the Biplolar/BiCMOS Circuits and Technology Meeting (BCTM).

Toshikazu Nishida received the B.S. degree in engineering physics and the M.S. and Ph.D. (in 1988) degrees in electrical and computer engineering from the University of Illinois, Urbana-Champaign. He is currently a member of the Interdisciplinary Microsystems Group, an Associate Professor with the Department of Electrical and Computer Engineering, and an Affiliate Associate Professor with the Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville. and is the holder of five US patents. His current research interests include solid-state physical sensors and actuators, transducer noise, strained semiconductor devices, and reliability physics of semiconductor devices. Dr. Nishida is a Distinguished Lecturer for the IEEE Electron Devices Society. He, with his colleagues and students, received three Best Paper Awards. He is also the recipient of the 2003 College of Engineering Teacher of the Year Award.