equivalent circuit method - IEEE Xplore

ICSE2004 Proc. 2004, Kuala Lumpur, Malaysia

Condenser Microphone performance Simulation using equivalent circuit method Bahram Azizollah Ganji and Burhanuddin Yeop Majlis, Member, IEEE MEMS Laboratory Institute of Microengineering and Nanoelectronics (IMEN) Universiti Kebangsaan Malaysia 43600 Bangi, Selangor, MALAYSIA Email: [email protected]

Abstract This paper presents the analysis of a condenser microphone for use in a hearing instrument and proposes a structure that can be realized using MicroElectroMechanical systems (MEMS) technology. The microphone uses a thin low stress polysilicon with an air gap and a silicon nitride perforated back plate. The aim is to develop the microphones with high sensitivity and low fabrication coast. The equivalent circuit method has been used to evaluate the performance of the microphone. The microphone diaphragm has a proposed thickness of 0.8 ,um, an area of 2.6 mm2, an air gap of 3.0 ftm and a 1.0 ,um thick back plate with acoustical ports. A 12.0 volt DC bias voltage is provided between the diaphragm and the back plate. A sensitivity of more than 45.0 mV/Pa is expected for the microphone, with a high frequency response extending to 20 kHz.

Keywords: MEMS, condenser microphone, circuit method, sensitivity, frequency response 1. INTRODUCTION

MICROPHONES are transducer that converts acoustic energy into electrical energy. The microphones are widely used in voice communications, hearing aids, noise, and vibration control [1]. The micromachining technology has been used to design and fabricate various silicon microphones. The silicon microphones have been based on the piezoelectric, pizoresistive and capacitive principles [2]. Piezoresistive microphones make use of a diaphragm incorporating four piezoresistors in a Wheatstone bridge

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configuration. A disadvantage of Piezoresistive transduction is relatively low sensitivity. Piezoelectric microphones use of a piezoelectric material that is mechanically coupled to diaphragm. A disadvantage of piezoelectric microphones is their relatively high noise level

[3, 4].

The capacitive microphones have been studied by many researchers because of their superior performances, e.g. high sensitivities, low power consumption, flat frequency responses in wide bandwidth, low noise level, stability and reliability [5]. There are mainly two branches in capacitive microphones. A condenser microphone and electret microphones. Electret microphones consist of an electret material, which can store a permanent charge, eliminating the need for external DC biasing. Most commercial microphones of this type use Teflon electret materials. Disadvantages of most electret microphones are the poor retention of electret charges, impossible to electrically regenerate any charges lost after their initial storage on the capacitor and incompatible with IC process [6]. Condenser Microphones consist of a variable gap capacitor. To operate such microphones need to be biased with a DC voltage (to form a surface charge) [7, 8]. The Condenser Microphones has demonstrated the highest achievable sensitivity and very low noise level. Also, condenser microphones are in increasing demand, thanks to their miniature size and the batch fabrication and integration feasibility [9, 10]. In this paper, the condenser microphone is studied. An electrical analog circuit is constructed to determine the microphone sensitivity. Optimal diaphragm edge width, thickness, and air gap are determined for


maximum sensitivity subject to pull-in voltage and processing constraints. 2. STRUCTURE OF CONDENSER MICROPHONE

Condenser Microphones generally consist of a diaphragm that is caused to vibrate by impinging waves of acoustic pressure, a back plate and air gap. In its simplest form, a diaphragm is stretched over a conductive back plate and supported by post so that there is a gap between the membrane and the back plate. Fig. I shows the basic structure of the condenser microphone. A metallized diaphragm is stretched by a tensile force, T, is put front of a fixed conducting back plate by means of a surrounding border which assures a separation distance, d, to create a capacitance with respect to the back plate and biased with a DC voltage. An acoustic wave striking the diaphragm causes its flexural vibration and changes the average distance from the back plate. The change of distance will produce a change in capacitance and charge, giving rise to a time varying voltage, V, on the electrodes. Diaphag

obtained using a highly perforated back plate. The shape of the frequency response of the microphone is determined by the damping and resonance behavior of the microphone structure, which depends mainly on the size ana stress of the diaphragm. 3. ANALYSES OF THE MICROPHONE USING EQUIVALENT CIRCUIT METHOD

The performance of the microphone depends on the size and stress of the diaphragm. Other parameters, such as air gap distance and the bias voltage, also affect the sensitivity. The dynamic behavior of the microphone can be calculated using and equivalent analog electrical model [1 I] as given in Figure 2. The acoustic force, F.omd, and flow velocity of air, Vm, are modeled as equivalent voltage and current sources, respectively. The air radiative resistance is defined as Rr, and the air mass is defined as Mr, The diaphragm mechanical mass is Mm, and its compliance is Cm. The air gap and back vent losses are represented by viscous resistances Rg and Rh, respectively. The air gap compliance is given by Ca [12].

C

R

Backpe

Ite

Fig. 1: The basic structure of the condenser microphone

Figure 2: Equivalent electrical circuit ofthe condenser microphone

A high mechanical sensitivity requires the use of a low stress material to construct a thin membrane with a large surface area and small air gap between the diaphragm and the back plate. Losses, due to the compression of air in the air gap, can be minimized by providing holes or acoustical ports in the back plate. Damping is caused by losses in the diaphragm and viscous losses associated with the air streaming in and out of the air gap. The perforation of the back plate to create acoustical ports provides a means to control streaming losses and therefore the damping characteristics of the microphone structure. A low damping property can be

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The diaphragm compliance depends on its flexural rigidity, D, and tension, T. The flexural rigidity of the diaphragm is given [13] by: D=

Et

12(1 - v2)

(1)

where E is Young's modulus of elasticity, t is the diaphragm thickness and i is Poisson's ratio. The tension, T, is determined by the residual stress of the diaphragm material, Or, is given by:


T = ct

(2)

32a2

m 6(2D2D + a2T)

The diaphragm deflection, W, can be approximated from the theory of vibration for a clamped edge rectangular plate as given by:

-DV4W + TV2W = pa 2

The equivalent acoustical mass element, Mm, is derived from the kinetic energy of the square diaphragm under the uniform loading as given by:

(3)

where p is mass per unit area (area density) of the diaphragm for a diaphragm thickness. The deflection of the square diaphragm for the first fundamental mode is:

W(x,y, r) = A sinxsin Y ej2f a

a

p(ID +r2 + frs=-( Ap a44 2a22 T

(5)

[14]:

(6)

and 8pOa3

r3;rvl;

(7)

where po is the air density, c is velocity of sound and is the angular vibration frequency (2Wf). The diaphragm compliance is equal to the average diaphragm deflection divided by the applied force. From the energy method, it is approximately: o

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The air gap viscosity loss in the air gap its compliance, Ca, are given by [14,151:

g

The acoustical impedance of the air in contact with the vibrating diaphragm has a radiative resistance, Rr, and an acoustical mass, Mr. for a square membrane, these can be approximated by

poa46L?2 = Rr 2rrc

+ a2T) Mm - 7t4p(27T2D 64T

(4)

where a is the diaphragm edge width. Substitution of Eq. (4) in Eq. (3) yields the first resonant frequency for the diaphragm: fre-

(8)

24

12i1a2(a a2 nd3nr 2 8

Ina 3 4 8

(9)

,Rg, and (10)

and

Ca= a

d

poc2a2a2

(1 1)

where n is the hole density in the back plate, a is the surface area occupied by the holes, -q is the air viscosity coefficient, d id the average distance, and po is the air density. The viscosity loss of the back plate holes can be given approximately as [16]:

Rh= 8qha2 74

(12) (12)

where h is the back plate thickness and r is the radius of the back plate hole. The sensitivity of the microphone is defined as the output voltage produced per unit of acoustical pressure applied to the diaphragm and is given by: S

VO P

Vba2

JiodZ,

(13)

where P is the applied sound pressure, Vb is the bias voltage between the diaphragm and the back plate. Zt is the total equivalent impedance of the circuit shown in Figure 2 and is given by:


Zi =Rr + jO(Mr + M) + jCOCm

1+

Rg+ R Rh)Ca j1(Rg +

(14)

The sensitivity of the microphone is hence function of the frequency.

a

From the above equation, we can see that sensitivity is a function of d2 and is proportional to the ratio of the bias voltage to the square of the pull-in voltage. Thus, by minimizing Vp and maximizing d the sensitivity can be increased. The capacitance between the diaphragm and the back plate can be expressed as:

4. OPTIMIZATION

C

A goal in our design is the maximization of sensitivity subject to fabrication and bias voltage constraints. The principal design variables are thus, the diaphragm size a, the diaphragm thickness t, the back plate thickness h, the air gap thickness d, the back plate hole radius r, and the surface area fraction occupied by the holes a. At low frequencies, the sensitivity of the microphone can be approximated as:

32Vba2 Ir6Td

(15)

The pull-in voltage for a clamped rectangular elastic plate under tension is approximately [17] given by:

Et3d3 21+ ( ovoa2 (+ -(I - v ) t) EQ VP P V2 \9) Et2 7J5(1_ )Oa4 =

64

64+

(16)

If t