High Performance Piezoelectric MEMS Microphones
20141123
Summary
-utilizing piezoelectric transduction
-Since the early 1980’s, researchers have been developing MEMS microphones that utilize both capacitive and piezoelectric transduction
-The
sensitivity of the device (for a microphone this is given in V/Pa) can then be used
to determine the equivalent noise at the input called the input referred noise. This
input referred noise is ultimately the noise of interest in any sensing system. Input
referred microphone noise is typically quoted as a sound pressure level (SPL) given
on an A-weighted scale (dBA). The A-weighted scale weights specific frequencies to
mimic the sensitivity of human hearing. The noise level is then converted to SPL, a
decibel scale referenced to 20 µPa, the nominal lower limit of human hearing.[The A-weighted scale & sound pressure level (SPL)]
Outdraw
High Performance Piezoelectric MEMS Microphones
by
Robert John Littrell
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
(Mechanical Engineering)
in The University of Michigan
2010
Doctoral Committee:
Professor Karl Grosh, Chair
Professor David R. Dowling
Professor Khalil Najafi
Assistant Professor Kenn Richard Oldham
TABLE OF CONTENTS
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
CHAPTER
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Capacitive and Piezoelectric MEMS Microphones . . . . . . . 1
1.2 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Piezoelectric Materials . . . . . . . . . . . . . . . . . . . . . . 9
1.6 Capacitive Microphone Embodiments . . . . . . . . . . . . . 11
1.7 Piezoelectric Microphone Embodiments . . . . . . . . . . . . 12
1.8 Gaps in the Literature . . . . . . . . . . . . . . . . . . . . . . 13
II. Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.1 Microphone Transducer Noise . . . . . . . . . . . . 16
2.1.2 Microphone Circuitry Noise . . . . . . . . . . . . . . 22
2.2 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.1 Cantilever Transducer Sensitivity . . . . . . . . . . 25
2.2.2 Diaphragm Transducer Sensitivity . . . . . . . . . . 31
2.3 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.1 THD of a Common Source Amplifier . . . . . . . . 36
2.3.2 THD Measurement Resonator . . . . . . . . . . . . 37
2.4 Combining Piezoelectric Elements . . . . . . . . . . . . . . . 38
2.5 Microphone Optimization . . . . . . . . . . . . . . . . . . . . 41
ii2.5.1 Cantilever Transducer . . . . . . . . . . . . . . . . . 42
2.5.2 Diaphragm Transducer . . . . . . . . . . . . . . . . 52
2.6 Packaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.7 Vibration Sensitivity . . . . . . . . . . . . . . . . . . . . . . . 57
III. First Generation Device . . . . . . . . . . . . . . . . . . . . . . . 59
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
IV. Second Generation Device . . . . . . . . . . . . . . . . . . . . . . 68
4.1 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2.1 Permittivity and Loss Angle . . . . . . . . . . . . . 75
4.2.2 Piezoelectric Coupling Coefficient (d31) . . . . . . . 76
4.2.3 Sensitivity and Noise Floor . . . . . . . . . . . . . . 77
4.2.4 Linearity . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
V. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1 Demonstrated Performance . . . . . . . . . . . . . . . . . . . 83
5.2 Further Performance Improvements . . . . . . . . . . . . . . . 85
5.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.5 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
CHAPTER I
Introduction
Microphones are used in a variety of everyday devices such as telephones and
computers but also have many specialized applications such as studio recording and
laboratory testing. Every year, more than two billion microphones are built for a
range of applications. Most of these microphones convert sound into an electrical signal
by utilizing capacitive transduction. Piezoelectric transduction, however, offers
unique advantages over capacitive transduction such as simplicity of fabrication and
linearity. These advantages have led to a further investigation of the typically cited
disadvantages of piezoelectric technology such as noise floor and sensitivity. Microphones
utilizing piezoelectric transduction have been designed, fabricated, and tested.
This work has led to new models of piezoelectric cantilevers and more accurate methods
for determining appropriate model assumptions. New, more accurate, methods
of determining piezoelectric coupling coefficients have been developed. Optimization
techniques which apply to a broad range of piezoelectric sensors have been identified.
Piezoelectric microphone advantages and limitations will be demonstrated.
1.1 Capacitive and Piezoelectric MEMS Microphones
Microelectromechanical systems (MEMS) is a term used to describe a variety of
electro-mechanical devices built by utilizing equipment and techniques originally de-
1
1
10−7 10−6 10−5 10−4 20
30
40
50
60
70
20kHz, Scheeper
10kHz, Ried
Diaphragm Area (m2)
Noise Level (dBA)
8.5kHz, Leoppart
10kHz, Royer
15kHz, Franz
10kHz, Bourouina
17kHz, Bergqvist
14kHz, Scheeper
9kHz, Zou
16kHz, Schellin
17kHz, Kressman
Capacitive Mics
Piezoelectric Mics
Figure 1.1: Capacitive and piezoelectric microphone noise levels as of December 2009.
veloped for integrated circuit manufacturing. These techniques, therefore, allow for
mechanical devices with very small, well defined features to be built. Since the early
1980’s, researchers have been developing MEMS microphones that utilize both capacitive
and piezoelectric transduction [1, 2]. Typically, MEMS piezoelectric microphones
have had a much higher noise floor (>10×) than capacitive microphones as seen in
Figure 1.1. This large disparity between capacitive and piezoelectric performance has
contributed to the adoption of capacitive transduction as the dominant technique for
MEMS microphones. Today, millions of capacitive MEMS microphones are built each
year.
The basic parameters of concern for any microphone, regardless of sensing technique,
are input referred noise (also measured as minimum detectable signal, signalto-
noise ratio, or noise floor), total harmonic distortion (THD, also measured as
maximum input level or dynamic range), and bandwidth (also measured as resonant
frequency). Also of interest are factors such as sensitivity, power consumption,
2
1.2 Noise
Noise is referred to as the inherent system fluctuations in system inputs or outputs
such as voltage, current, pressure, and displacement. This is separate from interference
from external signals because this interference is not an inherent limitation as it
can be removed. This work will primarily be concerned with thermal noise. Thermal
noise (also referred to as Johnson noise) was first documented by Johnson in 1928
[3]. Johnson noticed an electromotive force in conductors that is related to their temperature.
Nyquist then explained these results as a consequence of Brownian motion
[4, 5]. The theory of Nyquist was proved by Callen and Welton in 1951 [6]. Callen
and Welton also gave examples of mechanical systems that exhibit noise resulting
from mechanical dissipation [6]. Simply, any mechanism that converts mechanical
or electrical energy to thermal energy, such as a resistor or damper, also converts
thermal energy to mechanical or electrical energy. Therefore, any dissipative system
at a temperature above absolute zero will have noise associated with random thermal
agitation.
In a microphone/amplifier system, each significant noise source must be taken into
account. To do this, the effect of each noise source can be traced through the system
3to the output. The noise on the output is referred to as output referred noise. The
sensitivity of the device (for a microphone this is given in V/Pa) can then be used
to determine the equivalent noise at the input called the input referred noise. This
input referred noise is ultimately the noise of interest in any sensing system. Input
referred microphone noise is typically quoted as a sound pressure level (SPL) given
on an A-weighted scale (dBA). The A-weighted scale weights specific frequencies to
mimic the sensitivity of human hearing. The noise level is then converted to SPL, a
decibel scale referenced to 20 µPa, the nominal lower limit of human hearing.
The noise floor of capacitive microphones is typically limited by noise in the microphone
itself, the microphone preamplifier, or both. The dominant noise source in the
microphone is thermal noise resulting from damping seen by air entering and leaving
the small capacitive gap between the diaphragm and backplate [7]. The microphone
preamplifier noise is determined by the circuitry and can be affected by the device
capacitance, depending on the amplification scheme used [8, 9].
As a simplified example of capacitive microphone optimization, consider a MEMS
microphone consisting of a diaphragm and backplate. The backplate has holes to
reduce the resistance to air escaping the gap, thereby reducing the noise in the microphone.
If the microphone noise is dominant over the preamplifier noise, the number
of holes in the backplate can be increased or the distance between the backplate
and the diaphragm can be increased, both of which reduce air flow resistance and,
therefore, microphone noise [8]. Both of these changes also reduce the microphone
capacitance and sensitivity, thereby increasing the input referred preamplifier noise
[8]. It is beneficial to reduce the microphone noise at the expense of preamplifier noise
until the preamplifier noise becomes larger than the microphone noise. At the point
where both contribute equally to the overall noise of interest, the total microphone
noise has been minimized. This general microphone optimization technique can be
used for any capacitive microphone, MEMS or otherwise.
4Although several groups have developed piezoelectric MEMS microphones, the
fundamental limiting factor for noise floor remains unclear. Typical piezoelectric
microphones consist of multiple sensing electrodes due to the varying stress in piezoelectric
material on a diaphragm [1, 10, 11, 12, 13]. Researchers have exploited the
fact that these electrodes can be combined to trade off sensitivity for device capacitance
[10, 11]. When combined optimally, the combination of electrodes will preserve
the total output energy of the piezoelectric device but the capacitance can be adjusted
to minimize the effect of circuit noise on the microphone [10]. This method of minimizing
noise, however, neglects all noise coming from the piezoelectric microphone
and only minimizes the circuit noise.
The piezoelectric microphone will have thermal noise that stems from radiation
resistance [14] as well as structural damping [8]. The device will also have thermal
noise caused by the real part of the electrical impedance of the piezoelectric material
as described by Levinzon in a paper addressing piezoelectric accelerometers [15]. This
noise is determined by the loss angle (or dissipation factor) of the material and will
be filtered by the capacitance of the device [15]. Depending on the piezoelectric
material and amplification scheme used, this noise can be the dominant noise source
and cannot be ignored. This work will present complete microphone/amplifier system
noise models. This work will also present optimization techniques for reducing the
noise floor of piezoelectric devices. The noise models will be validated experimentally.
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