CHARACTERIZATION OF NOISE IN MEMS PIEZORESISTIVE MICROPHONES
By
ROBERT DIEME
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
2005
Copyright 2005
by
Robert Dieme
To my wife, my parents, and Rev. John D. Gillespie.
ACKNOWLEDGMENTS
I would like to thank my advisor, Dr. Toshikazu Nishida, for his guidance and
encouragement. I also would like to express my gratitude to Dr. Mark Sheplak, Dr. Gijs
Bosman, and Dr. Kevin Jones, for their ideas and encouragement. I would also like to
thank Dr. Louis N. Cattafesta III for help with my experiments. I also thank all
Interdisciplinary Microsystems Group (IMG) students for their help and support.
I thank my wife and parents for their prayers, support, and encouragement through
my study. Special thanks go to Rev. John D. Gillespie for his advice. Finally, I thank
God for the all of the graces He gives me.
iv
TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ................................................................................................. iv
LIST OF TABLES............................................................................................................ vii
LIST OF FIGURES ......................................................................................................... viii
ABSTRACT...................................................................................................................... xii
1
INTRODUCTION ........................................................................................................1
Motivation.....................................................................................................................1
Previous Work ..............................................................................................................2
Objectives and Outline .................................................................................................9
2
NOISE IN PIEZORESISTIVE MEMS MICROPHONES.........................................11
Noise and Noise Power Spectral Density ...................................................................11
Noise Sources .............................................................................................................12
Thermal Noise .....................................................................................................13
Low Frequency Noise..........................................................................................14
Hooge’s model .............................................................................................14
McWhorter’s model .....................................................................................15
Shot Noise ...........................................................................................................19
Piezoresistive Microphone..........................................................................................20
MEMS Piezoresistive Microphone Voltage Output............................................22
MEMS Piezoresistive Microphone Sensitivity ...................................................24
3
EXPERIMENTAL NOISE SETUP............................................................................25
Shielding .....................................................................................................................25
Wiring System ............................................................................................................29
Voltage Supply ...........................................................................................................32
Setup Noise.................................................................................................................35
Noise Figure................................................................................................................42
v
4
MICROPHONES NOISE MEASUREMENT ...........................................................45
Noise in Microphones.................................................................................................51
UF Piezoresistive Microphone ............................................................................51
UF Proximity Sensor ...........................................................................................54
Endevco Piezoresistive Microphone ...................................................................56
Kulite Piezoresistive Microphone .......................................................................57
Acoustic Calibration ...................................................................................................60
Frequency Response............................................................................................61
Linearity ..............................................................................................................63
Minimum Detectable Signal................................................................................66
Dominant Noise Source in MEMS Piezoresistive Microphones................................67
Acoustic Isolation Test ........................................................................................67
Membrane Contribution to 1/f Noise ..................................................................69
5
CONCLUSION AND FUTURE WORK ...................................................................72
APPENDIX: PIEZORESISTIVITY ..................................................................................74
LIST OF REFERENCES...................................................................................................77
BIOGRAPHICAL SKETCH .............................................................................................80
vi
LIST OF TABLES
Table
page
2-1
Manufacturers’ specifications for Endevco piezoresistive and Kulite
piezoresistive microphones ......................................................................................24
3-1
Noise power spectral density at 60, 120 and 180 Hz with one, two and three
faraday cages ............................................................................................................28
3-2
Pre-amplifier settings ...............................................................................................36
3-3
Spectrum analyzer setting ........................................................................................37
4-1
Our measured input and output impedances of UF piezoresistive microphone,
UF proximity, Kulite and Endevco ..........................................................................45
4-2
Frequency range during measurement .....................................................................47
4-3
Acoustic calibration results of UF microphone, UF proximity, Endevco and
Kulite microphones ..................................................................................................64
4-4
Sensitivity of the UF microphone, UF proximity, Endevco and Kulite
microphones under the same bias voltage (3 V) ......................................................65
4-5
Sensitivity of the UF microphone, UF proximity, Endevco and Kulite
microphones under same power dissipation (7 mW) ...............................................65
4-6
Minimum detectable signal (MDS) of UF microphone, UF proximity, Endevco
and Kulite microphones at different bias voltages ...................................................66
4-7
Minimum detectable signals (MDS) when the microphones are operated under
the same bias voltage (3 V) ......................................................................................67
4-8
Minimum detectable signals (MDS) when the microphones are subjected to the
same power dissipation (7 mW)...............................................................................67
A-1 Piezoresistive coefficients of silicon ........................................................................75
A-2 Transverse and longitudinal piezoresistance coefficients of silicon for <110>
direction....................................................................................................................76
vii
LIST OF FIGURES
Figure
page
2-1
Trapping-detrapping model for 1/f noise. ................................................................18
2-2
Piezoresistors configured in Wheatstone bridge. .....................................................21
2-3
Top view of a UF piezoresistive microphone...........................................................21
2-4
Cross-section of a UF piezoresistive microphone.....................................................21
3-1
PSD of UF microphone at 3 V shielded with one Faraday cage..............................27
3-2
PSD of UF microphone at 3 V shielded with two Faraday cages. ...........................27
3-3
PSD of UF microphone at 3 V shielded with three Faraday cages. .........................28
3-4
Power spectral densities of UF microphone at the same voltage bias with ground
loop, floating equipments and one ground connection. ...........................................29
3-5
Power spectral density of UF microphone with ground loop...................................30
3-6
Power spectral density of UF microphone with floating equipments. .....................31
3-7
Power spectral density of UF microphone with one ground connection. ................31
3-8
UF microphone biased with a power supply, zinc/carbon and lead acid batteries...33
3-9
UF piezoresistive microphone biased at 2.64 Volt with a power supply.................34
3-10 UF piezoresistive microphone biased at 2.64 Volt with zinc/carbon battery...........34
3-11 UF piezoresistive microphone biased at 2.64 Volt with lead acid battery. ..............35
3-12 Small signal representation of the setup noise. ........................................................37
3-13 Noise voltage power spectral density measurement setup. ......................................38
3-14 Voltage noise power spectral density of setup. ........................................................38
3-15 Noise current power spectral density measurement setup. ......................................39
viii
3-16 Current noise power spectral density of setup. ........................................................39
3-17 Experimental setup for a 1 kΩ metal film resistor. ..................................................40
3-18 Small signal analysis of voltage noise power spectral density of 1kΩ metal film
resistor. .....................................................................................................................40
3-19 Equivalent input voltage noise Svin in term of noise voltage. ..................................41
3-20 Equivalent input current noise SIin in term of noise current. ....................................41
3-21 Voltage noise PSD of a 1-kΩ metal film resistor without the subtraction of the
equipment setup noise. .............................................................................................42
3-22 Noise of the metal resistor with setup noise subtracted. ..........................................42
3-23 Noise figure of 1 kΩ metal film resistor using the SR560 low noise preamplifier..43
4-1
PSD of Kulite, Endevco, UF piezoresistive and UF Proximity sensor at 0 Volt
without setup noise...................................................................................................46
4-2
Noise figure of UF piezoresistive microphone, Kulite, Endevco, and UF
proximity sensor using the SR560 low noise pre-amplifier. ....................................46
4-3
Large signal representation of bias network. ...........................................................47
4-4
Small signal representation of bias network. ...........................................................48
4-5
Small signal representation of bias network using a ∆-Υ transformation................48
4-6
Experimental setup of noise measurement...............................................................49
4-7
Experimental setup for an AC bridge measurement. The mathematical
derivations have been obtained from Lorteije and Hoppenbrouwers.......................50
4-8
Power spectral density of UF piezoresistive microphone at different bias
voltages.....................................................................................................................51
4-9
Voltage dependence of PSD for UF piezoresistive microphone at 12 Hz and
binwidth 0.016 Hz....................................................................................................53
4-10 Hooge parameter of UF piezoresistive microphone.................................................53
4-11 Power spectral density of UF proximity sensor at different bias voltage (constant
reverse bias of -0.5 V). .............................................................................................54
4-12 Voltage dependence of PSD for UF proximity sensor at 12 Hz and binwidth
0.016 Hz. ..................................................................................................................55
ix
4-13 Hooge parameter of UF proximity sensor................................................................55
4-14 Power spectral density of Endevco microphone at different bias voltage. ..............56
4-15 Voltage dependence of PSD for Endevco microphone at 12 Hz and binwidth
0.016 Hz. ..................................................................................................................57
4-16 Power spectral density of Kulite microphone (without the temperature
compensation module) at different bias voltage. .....................................................57
4-17 Voltage dependence of power spectral density for Kulite microphone (without
the temperature compensation module). ..................................................................58
4-18 Kulite noise power spectral densities compared to the DC setup noise...................58
4-19 Comparison of power spectral densities of UF microphone, UF proximity
sensor, Endevco, and Kulite (without the temperature compensation module)
microphones biased at 2.6 V. ...................................................................................59
4-20 1/f noise figure of UF piezoresistive microphone, UF proximity sensor,
Endevco, and Kulite (without the temperature compensation module)
microphones biased at 2.6 V. ...................................................................................60
4-21 Experimental setup used with the normal incidence plane wave tube.....................61
4-22 Magnitude frequency response (normalized sensitivity) of Endevco, UF
proximity, Kulite (with and without the temperature compensation module) and
UF piezoresistive microphone..................................................................................62
4-23 Phase frequency response of Endevco, UF proximity, Kulite (with and without
the temperature compensation module) and UF piezoresistive microphone. ..........63
4-24 Linearity measurement of Endevco, proximity, Kulite (with and without the
temperature compensation module) and UF piezoresistive microphone. ................63
4-25 Sensitivity of Endevco, UF proximity, Kulite (with and without the temperature
compensation module) and UF piezoresistive as a function of pressure. ................64
4-26 Power spectral density of the Bruel and Kjaer 4138 condenser microphone and
of the UF piezoresistive microphone. ......................................................................68
4-27 Coherence function between the B&K and UF piezoresistive microphone.............68
4-28 Power spectral density of the UF piezoresistive proximity sensor with free
diaphragm.................................................................................................................69
4-29 Power spectral density of the UF piezoresistive proximity sensor with fixed
diaphragm.................................................................................................................70
x
4-30 Power spectral density of UF proximity sensor with free membrane at zero
biased voltage...........................................................................................................71
5-1
Focus ion beam (FIB) of an arc piezoresistor of the UF piezoresistive
microphone...............................................................................................................73
5-2
Transmission electron microscopy (TEM) results of an arc piezoresistor of the
UF piezoresistive microphone..................................................................................73
A-1 Polar plots of longitudinal and transverse piezoresistance coefficients for p-type
(100) silicon..............................................................................................................75
xi
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
CHARACTERIZATION OF NOISE IN MEMS PIEZORESISTIVE MICROPHONES
By
Robert Dieme
May 2005
Chair: Toshikazu Nishida
Major Department: Electrical and Computer Engineering
Microelectromechanical systems (MEMS) have provided many benefits in
measurement systems in acoustical, optical and electrical engineering. However, with the
desire for better MEMS sensor performance where high resolution and small device size
are required, multiple sensor parameters such as dynamic range, sensitivity, and noise
must be considered.
Our study focused on noise in MEMS devices. We examined noise sources in a
piezoresistive MEMS device. Careful noise measurements are needed to accurately study
noise in MEMS sensors. Techniques such as shielding, wiring system, biasing, and
extraction of setup noise from the total measured noise play fundamental roles in accurate
noise measurement. We measured and compared the noise power spectral densities of 4
piezoresistive microphones (2 university-experimental models and 2 commercial models)
at low frequencies (bias dependence, Hooge parameter) and noted their high frequency
thermal noise asymptote. We also measured microphone acoustic performance
parameters such as sensitivity, linearity, and minimum detectable signal using a plane
xii
wave tube. Excess noise at low frequencies in piezoresistive sensors with free and fixed
membrane was found to be of electrical origin.
xiii
CHAPTER 1
INTRODUCTION
The recent trend in integrated circuit (IC) technology is to fabricate small size
devices while improving their performance and reliability, and at the same time making
them affordable to consumers. Microelectromechanical systems (MEMS) are an
extension of IC technology that allows the fabrication of miniature systems such as
sensors and actuators, which are useful in a wide variety of engineering fields. These
miniature systems include transducers on the micrometer scale (for example,
piezoresistive pressure sensors, microphones, accelerometers, and cantilevers).
Motivation
Among many factors that limit MEMS performance transducers noise is critical
since it determines the minimum signal that can be detected. Reducing noise while
maintaining or improving device sensitivity will provide better signal-to-noise ratio and
lower minimum detectable signal.
However, to determine whether the sensor noise is at its theoretical minimum or if
a better design can achieve lower noise, one must first understand the fundamental noise
mechanisms and be able to take accurate noise measurements. Good data are obtained
when equipment are properly chosen and correctly used in a good, well-shielded
environment during the measurements. After establishing confidence in the accuracy of
the measurements, we used the resulting data to verify the contribution of different noise
sources in MEMS sensors, and to draw conclusions about their impact on sensor
performance. Knowing the most dominant noise source in sensors allow us to focus
1
2
effort on the real issue when designing a low-noise device. One may put much effort in
lowering a sensor noise floor, but end up being unsuccessful because the targeted noise to
be reduced was not a major contributor to the overall noise of the sensor, or because the
sensitivity was also reduced (leading to no improvement in the minimum detectable
signal).
Previous Work
Noise in MEMS sensors has been studied by many scientists who have focused on
specific noise sources, which they believe limit their device performance [1-4].
Optimization analysis to improve sensitivity and reduce noise was also done [5-7].
Harley and Kenny [5] showed methods used for fabricating high-sensitivity
piezoresistive cantilevers to improve their sensitivity, bandwidth, and noise. They
discussed geometric and process parameter effects on cantilever sensitivity, bandwidth,
and noise. Later [1], they gave a more detailed analysis for the optimization of
piezoresistive cantilevers. In their work, sensitivity, noise, bandwidth, and spring
constant were subjected to optimization based on cantilever geometry, process design,
and voltage operation. They provided formulas and graphs showing the effect of
thickness, length, and width on cantilever sensitivity. Thinner cantilevers yielded to an
improvement of the sensitivity. Cantilever leg lengths were chosen judiciously since a
trade off between sensitivity and low frequency noise is involved through the number of
carriers. For process optimization, shallow-doped cantilevers led to high noise, since the
number of carriers was small. Deep-doped cantilevers led to low noise because of the
large number of carriers. However, deep-doped cantilevers reduced the sensitivity since
the sensitivity efficiency β derived by Tortonese [8] was smaller. There is therefore a
trade off between noise and sensitivity. The same effect is seen with the choice of doping
3
concentration since the number of carriers plays a role in the noise and sensitivity
readings. Harley and Kenny confirmed the presence of bulk 1/f noise in their cantilevers.
They propose further studies on anneal to improve the quality of the crystal lattice in
order to reduce the bulk 1/f noise. They also suggested that piezoresistive devices be
biased according to their tolerance on power dissipation, to prevent either their
destruction or the decrease of their performance, since at low frequencies the noise
increases as the bias voltage squared.
Chau and Wise [6] analyzed the limits of silicon capacitive and piezoresistive
sensors when subjected to size reduction. The factors they discussed are pressure range,
pressure sensitivity, pressure resolution, and the effect of built-in diaphragm stress
(which mainly depends on parameters such as diaphragm length, diaphragm thickness for
piezoresistive microphone, and plate separation for capacitive microphone). Chau and
Wise stated that the pressure resolution is limited by various noise sources including
sources of both mechanical (Brownian noise) and electrical (piezoresistor thermal noise,
KT/C noise, circuit noise) origin. They provided tables showing the theoretical
performance of ultraminiature and ultrasensitive capacitive and piezoresistive sensors
assuming that the diaphragms are made of monocrystalline silicon and are free of built-in
stress. In the ultraminiature (scaled size) case, the performances of the devices were
analyzed as the diaphragms lengths are progressively reduced, while keeping steady
pressure ranges. As for the ultrasensitive (scaled sensitivity) sensors, the diaphragm
thickness was scaled down while the diaphragms length remained constant. Chau and
Wise stated that the capacitive sensors were limited by circuit resolution while
piezoresistive sensors were affected by offsets and temperature drifts in the
4
ultraminiature sensors case. In addition, ultraminiature capacitive sensors could not have
their sizes reduced as much as the sizes of their piezoresistive counterparts. However, the
theoretical study conducted by Chau and Wise reveals that ultraminiature capacitive
sensors have higher sensitivity that the piezoresistive ones. In the case of the
ultrasensitive sensors, the limits were set by pressure offsets and drift. Chau and Wise
study suggested that when high sensitivity is required, capacitive sensors are preferable
than the piezoresistive sensors. From the tables provided, among the noise mechanisms
present, Brownian noise was less significant than the thermal noise, kT/C noise and
circuit noise.
Chau and Wise [9] extensively studied Brownian noise in ultrasensitive capacitive
and piezoresistive sensors. A thorough analysis of a circular diaphragm surrounded by a
rarified gas in which the mean free path of gas molecules was larger than the diaphragm
diameter was done. The study was laid out in terms of deflection, kinetic and potential
energy, capacitance, stresses, damping coefficient and a constant K, which depends on
the properties and condition of the gas. As a result, a formula of the input pressure noise
due to Brownian motion for both ultrasensitive capacitive and piezoresistive sensors was
given for frequencies below the diaphragm fundamental resonance frequency. Chau and
Wise presented numerical computation of Brownian noise in both types of sensors
assuming that the built-in stress was negligible. The capacitive sensors revealed lower
noise that the piezoresistive ones. Furthermore, their study showed that Brownian noise
was less than the thermal noise of the piezoresistive sensors and the circuitry noise at low
frequencies. Chau and Wise concluded that Brownian noise was not a factor that could
5
prevent further miniaturization and sensitivity improvement of solid-state pressure
sensors.
Chau and Wise [9] result differs from the one made by Barabash and Cobbold [2].
In their investigation of the limitation of ISFET and silicon pressure transducers,
Barabash and Cobbold divided the noise sources of pressure transducers into two
categories: extrinsic (Brownian noise) and intrinsic noise (Johnson noise). The study of
the Brownian noise was conducted under the assumption that the mean free path is much
smaller than the diaphragm radius. Barabash and Cobbold derived formula of the total
mean square noise voltage and applied a specific example showing that the Brownian
noise voltage was much larger than the Johnson noise. Thus, they claimed that Brownian
noise was a limiting factor in silicon pressure transducers. However, Chau and Wise
concluded that Brownian noise was less significant than the other major noise sources
[9].
Hansen and Boisen [3] discusses noise in piezoresistive force microscopy. The
noises sources were divided into three categories: vibrational noise, Johnson noise, and
1/f noise. In their device modeling, Hansen and Boisen considered cases of ideal and real
devices with supported or free cantilever ends. The Johnson noise and flicker noise
originating from the piezoresistors were expressed with the cantilever physical
parameters. Hansen and Boisen point out the effect of bandwidth and temperature on the
total deflection noise power. The study of the temperature effect has been conducted by
analyzing the contributions of the thermal resistances of both the cantilever and the
supporting structure. Hansen and Boisen gave an expression of the total deflection noise
power as a function of temperature rise. For fixed design parameters of cantilevers,
6
comparisons of cantilevers with a single piezoresistor and full Wheatstone bridge
piezoresistors showed that the noise, when dominated by Johnson noise that is
temperature dependent, was lowered when a full Wheatstone bridge piezoresistors was
used. This reduction of noise level comes to the fact that when a full Wheatstone bridge
piezoresistors is used, the characteristic temperature parameter ∆Tc is reduced by half. A
table comparing the noise performance of different cantilever designs showed a reduction
in noise level for cantilevers with full Wheatstone bridge piezoresistor compared to
cantilevers with single piezoresistor.
Yu et al. [10], gave a detailed analysis on sensitivity and noise in piezoresistive
cantilevers. The results obtained serve as a guideline for optimization design of
cantilevers. Parameters involved in the process fabrication of cantilevers such as
piezoresistor geometry, doping concentration, annealing, bias voltage and material
properties are combined to study the trends in device performances. The experiments
show the influences of the parameters quoted above on the Hooge factor, gauge factor,
and minimum detectable deflection. In addition, the matrix of parameters was applied in
the fabrication of cantilevers with three different material properties: single-crystal
silicon, low-pressure chemical-vapor deposition (LPCVD) amorphous silicon and
microcrystalline silicon. A series of experiments, graphs, tables and plots were used to
draw conclusions of the optimization analysis. For instance, an increase in the volume of
the piezoresistors lowered the 1/f noise, which is said to be the dominant noise at low
frequencies. Their results showed that the doping dose did not affect much the Hooge
factor. However, its increase lowered the 1/f noise. In addition, annealing at 1050° C for
30 minutes on an amorphous silicon resistor revealed an improvement in the 1/f noise and
7
Hooge parameter compared to an annealing at 950° C for 10 minutes on the same resistor
type. Yu et al. suggested that single-crystal silicon; and LPCVD amorphous silicon and
microcrystalline silicon were suitable for the fabrication of cantilevers where high
resolution is required. However, their data showed that when the same annealing (950 oC
for 10 minutes) and doping dose (5x1014 cm-2) are applied single crystal piezoresistor
silicon had a lower Hooge parameter (5.7x10-6) than amorphous (1.3x10-3) and
microcrystalline silicon (1.8x10-3) piezoresistors.
Gabrielson [11] presented limiting factors in miniature acoustic and vibration
sensors. In addition to an analysis of the mechanical-thermal noise, he discussed other
noise in sensors (shot noise, 1/f noise, preamplifier noise, Johnson noise and optical
noise). Gabrielson proposed two techniques: one based on the frequency response of the
system or another based on a circuit simulation to estimate the noise of the sensor. In the
latter, an equivalent circuit representation of the mechanical system was used. Thus,
electrical and mechanical noise contributions were both evaluated.
In demonstrating the presence of a pure 1/f noise in the membrane motion of
condenser microphones and its effect on different microphones sizes, Zuckerwar and Ngo
[12] separated the membrane noise from the pre-amplifier noise. The microphone noise
was measured in an acoustic isolation vessel to keep the microphones at constant room
temperature and pressure. Zuckerwar and Ngo [12] provided a formula of the power
spectral density of the preamplifier output using a small circuit model of the
measurement setup (condenser microphone and pre-amplifier). Based on that formula,
Zuckerwar and Ngo extracted the membrane noise by subtracting the preamplifier noise
power, obtained when no external voltage was applied across the capacitor, from the total
8
noise power output of the pre-amplifier, when an external power supply was used to
apply a voltage between the capacitor membrane and back plate. The electromechanical
coupling is zero when no external voltage is applied to the capacitor’s plates. Based on a
plot illustrating the noise due to the membrane motion, the authors indicated the presence
of a 1/f noise in the membrane motion in the frequency range over which the 1/f noise is
dominant. From their experimental results, Zuckerwar and Ngo suggested that theories
of 1/f noise in the electrical domain could be extended to the mechanical domain.
In their most recent publication, Zuckerwar et al. [4] focused their background
noise studies on piezoresistive, electret condenser, and ceramic microphones for which
they provided small circuit representations of the noise in the microphone. In addition to
the well-known noise mechanisms present in piezoresistive microphone (mechanical
thermal noise, Johnson noise, and electrical 1/f noise), Zuckerwar et al. included a
mechanical 1/f noise, which they said is correlated to the diaphragm damping resistance.
Vandamme and Ooterhoff [13] supported the theory that 1/f noise is a bulk
phenomenon and computed the Hooge factor on ion-implanted resistors with different
annealing steps. Their results showed that high temperature annealing helped to reduce
the Hooge factor, therefore the 1/f noise. They attributed the decrease of 1/f noise to the
reduction of defects caused by high temperatures annealing. Belier et al. [14] showed
methods such as preamorphization and annealing to fabricate piezoresistors for
NanoElectroMechanical systems (NEMS) applications. The piezoresistors were
employed in the fabrication of a piezoresistive cantilever. Measurements of the 1/f noise
on boron fluorine (BF2) implanted piezoresistive cantilevers with and without
9
germanium preamorphization have been conducted. The results revealed lower 1/f noise
on the samples with germanium preamorphization.
Objectives and Outline
Today, the relevance of noise sources for pressure sensors is worth discussing since
sensor fabrication technology and applications fields face more challenges in terms of
resolution, sensitivity, bandwidth and operation. In the previous section, various
hypothesis and measurements are provided by authors to describe the limiting factors in
pressure sensors. Harley and Kenny et al. [1], in their study of noise in piezoresistive
cantilevers, which could be extended to piezoresistive microphones, found that electrical
1/f noise is the dominant noise factor among other noise sources such as thermal noise.
Barabash and Cobbold [2] postulated from their investigation that the Brownian
noise dominated the Johnson noise, and therefore was a limiting factor in the silicon
pressure transducers. Chau and Wise [9] concluded otherwise since their study suggested
that Brownian noise level was less significant than the thermal noise, kT/C noise and
circuit noise; therefore Brownian noise was not a factor that could prevent further
miniaturization and sensitivity improvement of solid-state pressure sensors.
Zuckerwar and colleagues’ challenge [4] was based on proving the presence of a
purely 1/f mechanical noise in the membrane motion of the pressure sensor and the
frequency over which it was dominant. Depending on the bandwidth, piezoresistor
fabrication process, and sensor dimension, the type of noise that limits the sensor
performance can vary. However, the relative presence and importance of some noise
sources such as the one proposed by Zuckerwar et al. need a particular attention.
Different authors have suggested various noise sources that limit the sensors
performance. One needs to find whether the dominant noise source is electrical or
10
mechanical of origin. This is important because when designing sensors with low
minimum detectable signal, noise level must be considered. We investigate the
mechanical and electrical noise sources in MEMS piezoresistive microphone using two
commercial piezoresistive pressure sensors: Kulite (MIC -093) and Endevco (8510B-1)
and two UF microphones: UF piezoresistive microphone [15, 16] and UF proximity
sensor [17].
CHAPTER 2
NOISE IN PIEZORESISTIVE MEMS MICROPHONES
Noise in MEMS sensors originates from different sources. The importance of
understanding their origin helps in the design criteria to improve the noise performance
and hence the fabrication of sensors with better signal to noise ratio and minimum
detectable signal. The fundamental noise mechanisms that potentially limit the
performance of the piezoresistive MEMS sensors are thermo-mechanical noise, Johnson
noise, 1/f noise, and shot noise.
Noise and Noise Power Spectral Density
Noise can be described as unwanted signals (acoustic, electrical) that contaminate
the desired signal. In the electrical domain, unwanted signals interfering with the desired
signal can originate from the environment (electromagnetic interference) or from the
electronic device itself via current or voltage fluctuations. These undesired signals can be
large enough to obscure the desired signal thus impeding its measurement. Techniques to
separate the signal of interest from external deterministic interferences include shielding
and proper wiring. However, intrinsic non-deterministic noise that originates from the
device cannot be avoided via shielding or proper wiring. Assuming proper shielding, the
intrinsic non-deterministic noise limits the lower part of the dynamic range of a device.
Since noise is a random process, analyzing it in the time domain does not give useful
information regarding its average magnitude. Therefore, we employ the power spectral
density function, which gives the magnitude of the random signal squared over a range of
11
12
frequencies for noise measurements. Power spectral density function as described by
Bendat and Piersol [18] is given in Equation 2-1.
Ψ 2x ( f , ∆f )
∆f → 0
∆f
Gx = lim
(2-1)
T
1 2
x ( t , f , ∆f )dt is the mean square value of a sample time
T →∞ T ∫
0
where Ψ 2x ( f , ∆f ) = lim
record between frequencies f and f + ∆f .
Noise Sources
Noise in semiconductor MEMS sensors is affected by various parameters such as
conductivity, defect density, temperature, doping concentration, and bias voltage. With
zero applied bias voltage and no external stimuli (light, thermal gradient) the
semiconductor is in equilibrium and its properties remain constant independent of time.
However, when bias or stimuli are applied, the semiconductor properties are no longer
constant, and the system is said to be in non-equilibrium. Noise in MEMS sensors can be
classified as equilibrium and non-equilibrium noise.
Solid-state materials can be divided in three major groups: conductors such as
aluminum, semiconductors such as silicon (elemental semiconductor) and gallium
arsenide (compound semiconductor), and insulators such as SiO2. Conductors have low
resistance. Their conductivity is on the order of 1x104 S/cm or higher. However,
insulators have very high resistance with conductivities on the order of 1x10-8 S/cm or
lower. Semiconductors are materials with conductivities lying between those of the
insulators and the conductors (1x10-8 and 1x104 S/cm). Doping, temperature, and
exposure to light can change the conductivity of semiconductor materials, rendering it
13
very attractive for electronic devices and transducers. Noises present in silicon
semiconductors based MEMS microphones are presented next.
Thermal Noise
Johnson noise describes voltage fluctuations at the terminal of a conductor or
semiconductor at equilibrium. These fluctuations are caused by the random vibrations of
charge carriers in equilibrium with the lattice at temperature, T. Work by Nyquist [19]
and Johnson [20] led to the expression of the thermal noise power spectral density given
in Equation 2-2.
Sth = 4 K B RT
⎡V 2 ⎤
⎢⎣ Hz ⎥⎦
(2-2)
where kB is the Boltzmann constant, R is the resistance, and T is the temperature in
Kelvin.
Electrical thermal noise is independent of bias voltage since the agitation of the
charge carriers by thermal lattice vibrations is present regardless of bias voltage.
However, an increase in the temperature induces more agitation of the carriers, hence
making the Johnson noise temperature dependent. Furthermore, Johnson noise frequency
independent because lattice vibrations are random, thus not related to any single time
constants.
Mechanical thermal noise is the mechanical analogue of electrical thermal noise.
By the fluctuation-dissipation theorem, any dissipative mechanism that results in
mechanical damping must be balanced by a fluctuation force to maintain macroscopic
energy balance, hence thermal equilibrium. In analogy with Equation 2-2, mechanical
thermal noise is given in Equation 2-3.
14
S mth = 4 K B RmT
⎡N 2 ⎤
⎢⎣ Hz ⎥⎦
(2-3)
where Rm is the equivalent mechanical resistance of the sensor.
Low Frequency Noise
Low Frequency noise is a frequency dependent non-equilibrium noise, which is
predominant at lower frequencies. It is also known as1/f noise. The mechanism that
generates 1/f noise is still an active area of research. Two widely discussed mechanisms
of 1/f noise are the fluctuation in the mobility (∆µ) described by Hooge [21] and the
fluctuation in the number of carriers (∆n) developed by McWhorter [22].
Hooge’s model
Hooge [21] originally conducted experiments on noise in homogeneous samples at
low frequency, which has an inverse frequency dependence (or 1/f). He suggested that
this 1/f noise at low frequency is a bulk phenomenon [21] and is due to fluctuations in the
mobility (∆µ)[23-25]. He gave an empirical formula for the noise power spectral density
of 1/f noise in his publications [21] as illustrated in Equation 2-4.
SV =
αV 2
Nf
⎡V 2 ⎤
⎣⎢ Hz ⎦⎥
(2-4)
Here α is an empirical material parameter varying from 1x10-6 to 1x10-3, V is the bias
voltage, N is the number of carriers and f is the frequency.
Hooge’s equation indicates a square bias voltage dependence for the low
frequency noise. Thus, this noise mechanism is only present when a voltage is applied
(for example, when a piezoresistive semiconductor MEMS microphone is biased). In
addition, the noise power spectral density is inversely proportional to number of carriers
15
N. Thus, the low frequency noise depends on the doping concentration Ndoping and
constant volume V, since N=Ndoping*V.
McWhorter’s model
McWhorter [22] conducted his experiments on germanium filaments and argued that
1/f noise is a surface effect. At the semiconductor surfaces and interfaces, physical
defects give rise to electronic traps that capture and emit charge. He postulated that 1/f
noise is caused by fluctuations of the number of charge carriers, due to trapping and
detrapping of charge carriers at these traps.
The difference between 1/f noise proposed by Hooge and McWhorter is illustrated
via the resistance fluctuations in a p-type resistor. Hooge [21] gives a spectral power
density of the fluctuation in the resistance R as shown in Equation 2-5.
SR
α
=
2
R
Nf
(2-5)
where S R is the noise power spectral density, α is a dimensionless parameter, f is the
frequency, and N is the number of carriers.
In a linear system, Ohm’s Law, V = R * I , holds and one can extend Equation 2-5 to
Equation 2-6 shown below.
S R SV S I
α
= 2 = 2 =
2
R
V
I
Nf
(2-6)
In a p-type resistor (p>>n) with length l, width w and thickness t, the resistance R is
R=
ρl
wt
[Ω]
(2-7)
16
Here the resistivity ρ of a p-type resistor is expressed as ρ =
1
σ
≈
1
σp
=
1
qµ p p
where σ
is the conductivity, q is the charge of the carrier, µ p is the hole mobility, and p is the
hole concentration. Thus, Equation 2-7 can be expressed in terms of mobility and hole
concentration as shown in Equation 2-8.
l
qwt µ p p
[ Ω]
(2-8)
∆µ p ∆ p
∆R
=−
−
R
µp
p
(2-9)
R=
Fluctuations in ∆R is expressed in Equation 2-9.
∆R =
∂R
∂R
∆µ p +
∆p
∂µ p
∂p
=−
=−
l
l
∆µ p −
∆p
2
qwt µ p p
qwt µ p p 2
R
µp
∆µ p −
R
∆p
p
and
where ∆µ p is the fluctuation in mobility and ∆p is the fluctuation in the carrier
concentration.
It is seen that fluctuations in R may be caused by fluctuations in µp, p or both
under bias conditions. The fluctuations in mobility can be explained as follows. The
time interval between two successive hole collisions is called the relaxation time or mean
free transit time and is denoted by τ. This relaxation time is determined by lattice and
17
impurity scattering. The mobility µp is related to the relaxation time τ as described in
Equation 2-10.
µp =
q⟨τ ⟩
mp
(2-10)
where mp is the hole effective mass, q is the charge of the carrier, and <τ>is the average
relaxation time.
Therefore, fluctuations in <τ> induce fluctuations in µp as shown in Equation 2-11.
∆µ p =
q∆⟨τ ⟩
mp
(2-11)
Under applied voltage bias, carriers drift in the resulting electric field giving rise to a
current I. This current is related to the mobility as shown in Equation 2-12 for a p-type
semiconductor resistor.
I pdrift = qµ p pε A
(2-12)
where ε is the electric field, and A is the cross-sectional area of the resistor.
Thus, from Equation 2-12, one sees that fluctuations in the current I pdrift are
induced by fluctuations in the mobility ∆µ p , which is in turn related to fluctuations in the
relaxation time ∆⟨τ ⟩ as shown in Equation 2-11. These time dependent fluctuations give
rise to 1/f noise.
The other possible source of 1/f noise is fluctuation in the number of carriers as
proposed by McWhorter [22]. The Lorentzian generation-recombination spectrum
resulting from the trapping and detrapping of the charges carriers at trap levels is given in
Equation 2-13 [26].
18
SGR ( f ) = AGR
τt
2
1 + ( 2π f τ t )
(2-13)
where AGR is proportional to the density of the trap levels, and τ t is the tunneling time
constant. Figure 2-1 describes the energy band diagram with two trap levels and their
E
I(t)=qµn
n
-
-
eAn(t)
-
Log PSD
(V2 /Hz)
associated Lorentzian spectra with a corner frequency at f 3dB =
1
2πτ
.
1/f
g-r 2
-
-
EC
g-r 1
g r
ET1
Thermal noise
E T2
A
f3dB
f3dB
Log f (Hz)
B
Figure 2-1. Trapping-detrapping model for 1/f noise. A) Energy band diagram of
trapping and detrapping at two trap levels, B) Lorentzian spectrum of two trap
levels in comparison with thermal noise.
Since electrons located in trap centers far from the conduction band require more
energy for generation-recombination to occur, τ is larger for deeper trap centers than
shallow trap centers as illustrated in Figure 2-1. Summing the noise power spectral
densities for a continuum of trap levels, we observe the 1/f noise shape up to the cut off
frequency where the curve rolls off as 1/f2. The 1/f noise observed at low frequency is
caused by the fluctuation in the number carrier in the conduction band due to trapping
and detrapping of carriers located at multiple trap levels.
Both Hooge’s and McWhorter’s 1/f noise models are actively used for low frequency
noise measurement in electronic devices [1, 10, 27].
19
However, since Hooge’s model describes the low frequency noise though
parameters (voltage, number of carrier, Hooge parameter) that are easily manipulated
during process fabrication or measurement of the electronic device, it is very attractive
for analysis. Designers can reduce the low frequency noise by adjusting or modifying
these parameters.
The validation of the Hooge model can be verified experimentally. First, one
observes that the noise power spectral density decays as the frequency increases. Second,
a graph of the noise power spectral density at a particular frequency versus the applied
voltage shows a voltage square dependence. In addition, for noise optimization purposes,
the extraction of the Hooge parameter α gives insight into the process fabrication quality
(defects density). Moreover, via simulation, one can choose the doping concentration
and resistor volume to reduce the 1/f noise through the number of carrier while maintain
good sensitivity (for example in MEMS piezoresistive microphones).
Later in this thesis, we use Hooge’s model to analyze the measured noise power
spectral densities and to verify whether the origin of the observed low frequency noise is
electrical or mechanical in the MEMS piezoresistive microphone.
Shot Noise
Schottky [28] investigated noise in vacuum tubes. He discovered a fundamental
noise mechanism arising from random emission of electrons from the cathode to the
anode which is termed shot noise.
In a semiconductor, when charge carriers cross a potential barrier independently
and randomly, fluctuations occur in the average current I. These fluctuations give rise to
shot noise which is a non-equilibrium noise. In particular, shot noise is observed in a p/n
junction due to the fluctuations in the average current I induced by the random crossing
20
of carriers over a potential barrier. The shot noise power spectral density is given in
Equation 2-14.
S I = 2qI
⎡ A2 ⎤
⎢⎣ Hz ⎥⎦
(2-14)
where q is the electron charge and I is the current.
Equation 2-14 shows that shot noise is directly proportional to the average current I,
hence is only present under bias conditions, and is frequency independent.
Piezoresistive Microphone
The transduction mechanism of the MEMS piezoresistive microphone is based on
converting acoustic energy into electrical energy. When pressure is applied to the
microphone, the diaphragm deflects producing a change in the resistance of the four
piezoresistors configured in a Wheatstone bridge as shown in Figure 2-2 and located at
the diaphragm edge where the stress is maximum. The change is the resistance is due to
a property of material known as piezoresistivity. Information on piezoresistivity is
provided in the Appendix. Two piezoresistors are positioned to sense the stress parallel
to the current flow while the other two are placed to sense the stress perpendicular to the
current flow. The Wheatstone bridge provides a null voltage across the bridge at zero
pressure, Vout = 0 , when the bridge is balanced, i.e. R1 = R2 = R3 = R4 . When there is
pressure incident on the microphone, the diaphragm deflects producing equal absolute
value resistance change across the four piezoresistors. The resistance change in R1
and R3 have opposite signs to that of R2 and R4 . These resistance change produce a
differential output voltage Vout = V1 − V2 across the bridge, where V1 and V2 are equal in
magnitude but have opposite signs.
21
Figure 2-2. Piezoresistors configured in Wheatstone bridge.
Top and cross-sectional views of a UF piezoresistive microphone are shown
respectively in Figure 2-3 and 2-4 [16].
Bond Pad
(250 µm x 250 µm)
Arc Resistor
Diaphragm
(1 mm x 1 µm)
Vent Channel
(10µ m x 10µ m x 9.5 mm)
Taper Resistor
Figure 2-3. Top view of a UF piezoresistive microphone [16].
p+ Silicon
)
Nitride
(2000 Å)
(1x1020 cm-3
Oxide
(550 Å)
Aluminum
(1 µm)
Nitride
(1 µm)
n-Si
Figure 2-4. Cross-section of a UF piezoresistive microphone [16].
Oxide
(7000 Å)
22
Details of the design of this piezoresistive microphone are presented by Saini
[15]. In this analysis, it is assumed that the four piezoresistors of the Wheatstone bridge
have equal unstressed resistance, thus we have a balanced bridge at zero applied pressure.
MEMS Piezoresistive Microphone Voltage Output
When pressure or force is applied to the microphone’s membrane, it induces
stress and resulting strain on the membrane. These physical phenomena, stress and
strain, have an impact on the piezoresistors located at the edge of the membrane where
the stress is maximum. Strain is the change per unit length of the piezoresistors and is
expressed as shown in Equation 2-15.
ε=
∆L
L
(2-15)
where ∆L is the change in the original length of the piezoresistor and L is the original
length of the resistor.
The strain sensitivity, which is called the gauge factor G0, is expressed as shown in
Equation 2-16.
G0 =
( ∆R
R0 )
ε
(2-16)
where ∆R is the chance of resistance R and ε is the strain.
The resistance of a semiconductor resistor is given in Equation 2-17.
R=ρ
l
wt
(2-17)
where ρ is the resistivity, and l , w and t are respectively the length, width and thickness
of the resistor.
The expression
∆R
is obtained by differentiating Equation 2-17 and dividing the
R
23
resulting expression by the resistance R as illustrated in Equation 2-18.
∆R ∆ρ ∆l ∆w ∆t
=
+ −
−
R
ρ
l
w
t
(2-18)
Using the Poisson’s ratio, the strain sensitivity G becomes
G=
∆R
ε
∆ρ
R = (1 + 2υ ) +
ρ
(2-19)
ε
In Equation 2-19, (1 + 2υ ) is due to the geometry change and
∆ρ
ρ
is due to the
piezoresistive effect. For metal, the piezoresistive effect is negligible and therefore the
gauge factor can be expressed in term of its geometrical change only as shown in
Equation 2-20.
G=
∆R
ε
R = (1 + 2υ )
(2-20)
Since υ is less than 0.5, G for metal is about two. For semiconductor, the gauge factor,
G, is dominated by the piezoresistive effect
∆ρ
ρ
and can have a magnitude in the range
of 100. The expression of sensor output voltage ∆Vout given in Equation 2-21 describes a
linear relation between the input pressure on the membrane of the microphone and the
output voltage of the Wheatstone bridge configuration.
∆Vout = G0εVbias
(2-21)
Using Equation 2-19, we express the bridge output voltage ∆Vout in terms of the change in
resistance ∆R , the resistance R and the bias voltage Vbias.
∆Vout =
∆R
Vbias
R
(2-22)
24
Hence with application of an external bias the piezoresistive microphone provides a
linear output voltage related with resistance change. If a mechanical transfer function
relating ∆R to pressure is linear, then a linear acoustic transducer is achieved.
MEMS Piezoresistive Microphone Sensitivity
The sensitivity of a MEMS piezoresistive microphone is given by the ratio of the
output voltage to the input pressure. The normalized sensitivity, which is the sensitivity
divided by the bias voltage is shown in Equation 2-23.
1 Vout
1 ∆Vout 1 ∆R
S=
≈
=
Vbias p Vbias p
R p
(2-23)
where Vbias is the voltage applied to the microphone, ∆Vout is the differential output
voltage, and ∆R is the resistance modulation of the piezoresistor.
In the next chapter, the experimental setup for careful noise measurement is
discussed. Noise measurement on the UF piezoresistive microphone and three other
sensors: UF proximity sensor, Endevco piezoresistive microphone and Kulite
piezoresistive microphone will be discussed in Chapter 4.
Table 2-1. Manufacturers’ specifications for Endevco piezoresistive and Kulite
piezoresistive microphones
Parameters
Endevco
Kulite
Maximum voltage (V)
18
15
Input impedance (Ω)
2060
3112*
Output impedance (Ω)
1832
1152
Sensitivity (µV/Pa)
26.9
4.3
*Input impedance of Kulite microphone with a temperature compensation module.
CHAPTER 3
EXPERIMENTAL NOISE SETUP
In this chapter, we will explore experimental setup techniques to accurately
measure noise power spectral density of a device under test. To reach our goal stated
above, we justify the use of three Faraday cages, show the effect of ground loops,
evaluate the noise levels when biasing the device under test with different types of
voltage supply, determine the setup noise, and extract the noise of the device under test.
The equipment used for the measurement are: three Faraday cages, low noise
preamplifiers(SRS 560 and Brookdeal 5004), a dynamic signal analyzer (SRS 785), lead
acid batteries, standard AA batteries, line-powered regulated power supply, metal film
resistors, double shielded coaxial cables (RG-223/U), and BNC connectors.
Shielding
To reduce signal contamination from non-intrinsic noise sources, such as radio
signals (AM, FM, Radar) at high frequencies, and power line interference at 60 Hertz and
harmonics, shielding is necessary. It is accomplished by enclosing the equipment inside
a Faraday cage, which is a conducting material box of sufficient thickness, to attenuate
the electromagnetic radiation. The latter results from the combination of both electric
and magnetic fields. Electrical current is produced in a conductor inductively through a
time-varying magnetic field or capacitively via an electric field.
Michael Faraday demonstrated in 1836 that charges are located on the outside
surface rather than the interior of a conductor. This discovery is the reason why metal
25
26
boxes are used as shielding devices. However, each material has a penetration distance
of electromagnetic radiation called the skin depth as shown in Equation 3-1.
δ=
c
2πσµω
(3-1)
where c is the speed of light, σ is the electrical conductivity, µ is the permeability, and ω
is the angular frequency. At low frequency, the skin depth is larger, therefore shielding
becomes more difficult.
In our measurement setup, we covered our boxes with magnetic shielding foils [29]
to improve the shielding capacity. For instance, at 10 Hz, the permeability of the
magnetic shielding foil is 10,000. A plot illustrating the permeability versus frequency of
the shielding foil and the material specification are given in [29]. From manufacturer’s
specification sheet, the chemical composition of the magnetic shielding foils is nickel
(80%), iron (15%), molybdenum (5%) and small amounts of sulfur, carbon, manganese,
silicon, and phosphorous, and its thickness is 104.14 µm. The effect of three successively
enclosed Faraday cages is shown by plotting the power spectral density of a device under
test, showing the decrease in the electromagnetic interference pick up with increase in
number of Faraday cage. We used three thin Faraday cages because it is easier to
fabricate and implement than one thick Faraday cage. We provide three noise power
spectral densities of the UF microphone when one, two and three shielded boxes are used.
The microphone is biased at three volts with a lead acid battery and metal film resistors in
an implementation of a voltage divider. The effects of one, two, and three Faraday cages
are shown and compared in Figures 3-l, 3-2 and 3-3. Note that the curves are shown
27
separately to allow comparison of the magnitude of the interference peaks. When one
Faraday is used, the power spectral density of the UF microphone is shown in Figure 3-1.
1.E-10
1.E-11
2
Sv (V /Hz)
1.E-12
1.E-13
1.E-14
1.E-15
1.E-16
1.E-17
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-1. PSD of UF microphone at 3 V shielded with one Faraday cage.
In Figure 3-1, one can observe a poor shielding. The 60 Hz harmonics are present
up to 1 kHz. Better shielding is necessary to minimize the interferences. A similar
measurement as the one above is performed except that in this case, we use two Faraday
cages instead of one. Figure 3-2 shows the result of the experiment. The 60 Hz
harmonics have decreased in number and their magnitudes lowered. In this case, we note
that the low noise amplifier has been shielded along with the device under test.
1.E-10
1.E-11
2
Sv (V /Hz)
1.E-12
1.E-13
1.E-14
1.E-15
1.E-16
1.E-17
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-2. PSD of UF microphone at 3 V shielded with two Faraday cages.
28
One can obtain a cleaner power spectral density by using three Faraday cages in
Figure 3-3. Such experiment is performed under the same conditions as the previous
measurements.
1.E-10
1.E-11
2
Sv (V /Hz)
1.E-12
1.E-13
1.E-14
1.E-15
1.E-16
1.E-17
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-3. PSD of UF microphone at 3 V shielded with three Faraday cages.
Using three Faraday cages, we observe a single peak at 60 Hz, with magnitude
lower than the previous measurements. Table 3.1 summarizes the noise power spectral
density at 60, 120 and 180 Hz when the measurement is conducted with one, two and
three faraday cages.
Table 3-1. Noise power spectral density at 60, 120 and 180 Hz with one, two and three
faraday cages
Number of Faraday
PSD at 60 Hz
PSD at 120 Hz
PSD at 180 Hz
cages
(V2/Hz)
(V2/Hz)
(V2/Hz)
1
1.86E-11
5.63E-12
1.18E-13
2
1.50E-13
2.71E-15
4.31E-15
3
1.96E-14
1.59E-15
1.00E-15
From Table 3-1, one observes a drop in noise power spectral densities at 60, 120
and 180 Hz as the number of Faraday cages increases. Good shielding could also have
been obtained with only one Faraday that has a shielding capacity equal to or higher than
the three cages used in our experiment combined.
29
Now that we have a technique for proper shielding of the device under test, we will
explore the effect of grounding.
Wiring System
To prevent electromagnetic contamination of noise measurement, one should pay
particular attention to the wiring system of the setup. Bad wiring system can contribute
to the enhancement of signal contamination by external noise sources. Two examples of
bad wiring systems are ground loop and having no ground at all. In both cases, the 60 Hz
interference is significant. In addition to the unclean power spectrum obtained when no
ground connection is used, the latter constitutes a safety issue. Electrocution can result
since during an electrical fault there is no path for the current to flow to ground. Usually,
one ground connection is optimal. Figure 3-4 shows noise power spectral densities of the
UF microphone at the same voltage bias when ground loop, floating equipment and one
ground connection are implemented.
1.E-10
2
Sv (V /Hz)
1.E-11
Ground loop and Floating equipments
1.E-12
1.E-13
1.E-14
Single ground
1.E-15
1.E-16
1.E-17
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-4. Power spectral densities of UF microphone at the same voltage bias with
ground loop, floating equipments and one ground connection.
In the figure above, we cannot clearly differentiate the ground loop plot to the no
ground and one ground plot since their spectral densities overlap. However, there are
differences in electromagnetic contaminations. Separate plots will be provided for
30
clarification. To investigate the effect of a ground loop, long power lines (~ 12 m)
connected at different building outlets are used to power the equipments. In addition, a
long single shielded BNC (~ 0.61 m) connected the device output to the low-noise
amplifier and the spectrum analyzer. In this setup, we use the best shielding obtained
from the last section, three Faraday cages, and a lead acid battery provides the bias
voltage through a network of metal film resistors used in the voltage divider. The
resulting noise power spectral density of this setup is shown in Figure 3-5.
1.E-10
2
Sv (V /Hz)
1.E-11
1.E-12
1.E-13
1.E-14
1.E-15
1.E-16
1.E-17
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-5. Power spectral density of UF microphone with ground loop.
In the ground loop figure, one observes power line harmonic peaks at discrete
frequencies in multiples of 60 Hz up to 2 kHz and also leakage at certain frequencies.
According to Faraday’s Law, the change in the magnetic flux in a coil of wire will induce
a voltage within the coil of wire. This mechanism takes place in the setup from which
Figure 3-5 has been measured. In fact, a changing AC field, originated from the power
line, gives rise to potentials at multiple points in the BNC cables (~ 0.61 m) between the
various building ground connections.
Next, the effect of floating all the equipments is shown in Figure 3-6. In this case,
power line harmonics are also seen. Even though there is no ground connection for all
31
the equipment, the external noise picked up by the long power lines and exterior surface
of the Faraday cages contaminate the signal.
1.E-10
2
Sv (V /Hz)
1.E-11
1.E-12
1.E-13
1.E-14
1.E-15
1.E-16
1.E-17
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-6. Power spectral density of UF microphone with floating equipments.
To reduce noise contamination due to the environment, we use one ground
connection, short power lines (~ 1.27 m) and BNC cables (~ 0.15 m) along with the three
Faraday cages. The result of such a setup is illustrated in Figure 3-7.
1.E-10
2
Sv(V /Hz)
1.E-11
1.E-12
1.E-13
1.E-14
1.E-15
1.E-16
1.E-17
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-7. Power spectral density of UF microphone with one ground connection.
In the plot above, most of the 60 Hz and harmonic interference frequency peaks
are no longer present and the remaining are reduced. This is because there is no ground
loop, therefore a reduction of the 60 Hz magnetic coupling, and most of the
electromagnetic interference not blocked by the Faraday cage is terminated at one single
ground point. The suppression of ground loop constitutes a major effect in the cleanness
32
of the signal. The difficulty to completely suppress the 60 Hz interference at low
frequency comes from the fact that the skin depth is larger in that range, therefore
penetration of electromagnetic radiation in the conductor takes place.
Therefore, the wiring system is important when performing noise measurements.
It is important to make the proper choice of short and shielded cable while using a
Faraday cage to shield the device under test against extrinsic noise sources. It is also
important to provide a path to a single ground point to avoid ground loops and to limit
risk of electrocution.
Voltage Supply
The choice of voltage supply used when performing noise measurement of a device
is important. The voltage supply can add noise to the measurement. To illustrate the
above statement, noise measurements were performed on a UF piezoresistive microphone
at 2.64 Volt bias for three sources: (1) a line-powered regulated power supply, (2)
zinc/carbon, and (3) lead acid batteries as shown in Figure 3-8. One can realize from the
plot that using a line-powered power supply introduces significant electromagnetic
interference. The power spectral densities obtained using zinc/carbon and lead acid
batteries show less 60 Hz harmonics contaminations. Since it is difficult to distinguish
them when plotted together, separate plots of all the measurements will be given for
clarification of the data.
When a line-powered power supply is used to bias the UF microphone, the
resulting plot reveals the presence of strong 60 Hz harmonics even at high frequencies.
This is due to the fact that the power supply connected to the 60 Hz line power of the
building magnetically couple the 60 Hz fundamental and harmonics through an internal
transformer.
33
1.E-09
1.E-10
2
Sv( V /Hz)
1.E-11
1.E-12
1.E-13
1.E-14
Power supply
1.E-15
1.E-16
1.E-17
1.E+01
Zinc/carbon and lead acid battery
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-8. UF microphone biased with a power supply, zinc/carbon and lead acid
batteries.
In addition, multiple grounds arise from the fact that there are two ground points,
one for the spectrum analyzer and a separate one for the power supply. One could
operate the power supply in floating mode to obtain one single ground point from the
spectrum analyzer. However, in that setup not only is there safety implications, but also
the 60 Hz power line still contaminates the signal with 60 Hz and harmonic frequencies.
Therefore, no improvement in the power spectral density is observed. Figure 3-9 shows a
plot of the noise power spectral density when a line-powered power supply is used as the
bias voltage. To reduce 60 Hz power line interference contamination, batteries may be
used as the bias voltage. However, the choice of battery plays an important role in the
noise level. Plots of power spectral densities at 2.64 volts using zinc/carbon and lead
acid batteries are presented in Figures 3-10 and 3-11 respectively.
Although both batteries types help reduce noise contamination, the lead acid
battery is a better choice between the two since carrier trapping/detrapping is less
dominant in the liquid (lead acid battery) than in the granular solid (Zinc/carbon battery).
In addition, two advantages of using a lead acid battery are the larger capacity (long
lasting) and the capability to recharge since noise measurements can be lengthy in time,
34
usually when the binwidth is very small and the number of averages large for better
accuracy and require a reliable source of power. In fact, the resistance of a decaying
battery increases, thus is likely to add noise into the signal.
1.E-09
1.E-10
2
Sv ( V /Hz)
1.E-11
1.E-12
1.E-13
1.E-14
1.E-15
1.E-16
1.E-17
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-9. UF piezoresistive microphone biased at 2.64 Volt with a power supply.
1.E-09
1.E-10
2
Sv( V /Hz)
1.E-11
1.E-12
1.E-13
1.E-14
1.E-15
1.E-16
1.E-17
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-10. UF piezoresistive microphone biased at 2.64 Volt with zinc/carbon battery.
Using the results obtained from investigating shielding, wiring system and bias
supply, we are confident on the necessary techniques for proper noise measurement. In
the next section, in addition to the equipment setup, the internal settings of the low-noise
amplifiers and spectrum analyzer are provided.
35
1.E-09
1.E-10
2
Sv ( V /Hz)
1.E-11
1.E-12
1.E-13
1.E-14
1.E-15
1.E-16
1.E-17
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-11. UF piezoresistive microphone biased at 2.64 Volt with lead acid battery.
Setup Noise
In this section, we evaluate the setup noise. The setup noise power spectral density
will be subtracted from the total power spectral density measured for the device under
test. The preamplifier and spectrum analyzer setup noise will be given along with the
bias voltage and detailed diagrams of the equipment setup.
The setup noise is the contribution to the measured noise by the equipment used
during the measurement. We measure both the current and voltage noise power spectral
densities of the setup. In these measurements, the pre-amplifier and the spectrum
analyzer are configured as shown in Table 3-2 and Table 3-3. The coupling is set to AC
because we are interested in the time-varying signal. The differential inputs A-B allow
the measurement of the microphone output voltage. If single ended input was used, then
one of the output signals would have been set to ground.
In addition, increased dynamic range is provided by the differential mode due to
improved common mode noise rejection. When the SRS 560 is used during
measurement, the filter is set as a band pass filter with lower and higher limits at 0.03 Hz
and 300 KHz with ± 6 dB/octave roll off.
36
Table 3-2. Pre-amplifier settings
Parameters
SRS 560
Coupling
AC
Inputs
A-B
Bandwidth
0.03 Hz – 300 KHz
Gain
1000
Input
100 MΩ, 25 pF
Output
50 Ω
Brookdeal 5004
AC
A-B
0.5 Hz – 1 MHz
1000
5MΩ, 50 pF
1 KΩ
The gain is set to 1000 ensuring that the output signal of the preamplifier is higher
that the noise floor of the spectrum analyzer allowing accurate noise measurement. The
input and output impedance of the pre-amplifiers are specified by the manufacturers.
They are relevant to the analysis of the current and voltage setup noise, as we will see
later in this section.
The setup of the spectrum analyzer is illustrated in Table 3-3 below. The coupling
is set to AC since we are interested in small signal fluctuation. In the spectrum analyzer,
the single-ended input A is chosen. A Hanning window is selected for the measurement
of the random signal because it provides good selectivity and reduces power spectral
density leakage.
A list of spans, FFT lines and bin widths is given in Table 3-3. The power spectral
density is obtained by overlapping the measurements of the different spans. At low
frequencies, the binwidth is smaller to ensure better frequency resolution and therefore
good accuracy of the measurements. The first 10% of each measurement span are
truncated to minimize error due to leakage at the lowest frequencies since the digital
window filter, Hanning, is not infinitely sharp. Multiple such spans are overlapped to
obtain the overall power spectral density. LabView is used to automate the
measurements. The amplifier used in the remaining section to illustrate the setup noise is
the SRS 560. The same principle may be applied to the Brookdeal amplifier.
37
Table 3-3. Spectrum analyzer setting
Parameters
Settings
Coupling
AC
AC
Input
A
A
Window
Hanning Hanning
Span (Hz)
100
400
FFT Lines
800
800
Binwidth (Hz) 0.125
0.5
Averages
1700
5000
AC
A
Hanning
1600
800
2
10000
AC
A
Hanning
12800
800
16
30000
The small signal representation of an amplifier is shown in Figure 3-12. The
amplifier noise model consists of input referred noise sources represented as voltage and
current noise sources and an ideal noise-free amplifier. The input impedance of the
amplifier is represented as Zin described in Figure 3-12.
Sva
Spectrum Analyzer
(SR785)
Pre-Amp
(SR560)
Sia
Zin
G
Figure 3-12. Small signal representation of the setup noise.
The voltage noise source Sva of the pre-amplifier, given by Equation 3-2, is
obtained by shorting the input of the pre-amplifier, which allows the cancellation of Sia.
In this case, the source resistance seen by the input of the pre-amplifier is very low
(RS→0). The resistance measured at the input is 0.26 Ω. Figure 3-13 shows the voltage
noise power spectral density measurement setup.
Sva =
Svout
G2
⎡V 2 ⎤
⎢⎣ Hz ⎥⎦
(3-2)
38
Shielded Box
Shielded Box
A
Pre-Amp
(SR560)
Spectrum
A Analyzer
(SR785)
B
Chassis
Computer
(LabView)
AC Out
AC Out
Figure 3-13. Noise voltage power spectral density measurement setup.
The voltage power spectral density measured is shown in Figure 3.14.
1.E-15
2
Sv (V /Hz)
1.E-14
1.E-16
1.E-17
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-14. Voltage noise power spectral density of setup.
To measure the current noise power spectral density of the setup, the input of the
pre-amplifier is open circuited. This permits cancellation of the voltage noise source Sva,
allowing measurement of only the current power spectral density Sia. The setup of this
experiment is shown in Figure 3-15. The source resistance for the open-circuit case seen
by the input of the amplifier is infinite. Equation 3-3 gives the current noise power
spectral density.
39
Sia =
Svout
S
= iout2
2
2
RinG
G
⎡ A2 ⎤
⎣⎢ Hz ⎦⎥
(3-3)
where Svout is the measured voltage noise power spectral density, Rin is the input
impedance of the pre-amplifier, and G is the gain of the pre-amplifier. The measured
current power spectral density is shown in Figure 3-16.
Shielded Box
Shielded Box
A
Pre-Amp
(SR560)
Spectrum
A Analyzer
(SR785)
B
Chassis
Computer
(LabView)
AC Out
AC Out
Figure 3-15. Noise current power spectral density measurement setup.
1.E-31
2
Si (A /Hz)
1.E-30
1.E-32
1.E-33
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-16. Current noise power spectral density of setup.
The experimental setup with a 1 kΩ metal film resistor as source resistance is
shown in Figure 3-17.
40
Shielded Box
Shielded Box
Shielded Box
A
Rmfr
Pre-Amp
(SR560)
A
B
Spectrum
Analyzer
(SR785)
Chassis
Computer
(LabView)
AC Out
AC Out
Figure 3-17. Experimental setup for a 1 kΩ metal film resistor.
The noise equivalent circuit corresponding to Figure 3-17 is shown in Figure 3-18.
Sva
Pre-Amp
(SR560)
Rdut
Sia
Zin
G
Spectrum Analyzer
(SR785)
SVRdut
Figure 3-18. Small signal analysis of voltage noise power spectral density of 1kΩ metal
film resistor.
Sva and Sia are respectively the voltage and current noise power spectral densities of the
pre-amplifier, and SVRdut is the noise source associated with the device under test, in our
case a 1 kΩ metal film resistor.
Figure 3-18 can be represented by an equivalent input noise in term of noise
voltage or noise current as shown respectively in Figures 3-19 and 3-20. The voltage
noise PSD of the device under test, Rdut, can be extracted by subtracting the noise
contribution of the setup as shown in Equation 3-4.
41
S dut = Svout − S setup
⎡V
⎤
⎢⎣
Hz ⎥⎦
(3-4)
Svin =Sva+Sia (Rdut//Zin)2
Pre-Amp
(SR560)
Rdut
Zin
Spectrum Analyzer
(SR785)
G
SVRdut
Figure 3-19. Equivalent input voltage noise Svin in term of noise voltage.
SIin =Sia+Sva /(Rdut//Zin)2
Pre-Amp
(SR560)
Rdut
Sia
Zin
G
Spectrum Analyzer
(SR785)
SIRdut
Figure 3-20. Equivalent input current noise SIin in term of noise current.
The plot of the noise voltage power spectral density of the setup and power
spectral density of a 1 kΩ metal film resistor without subtraction of the equipment setup
noise is shown in Figure 3-21. Once the setup noise is subtracted from the total output
noise, the remaining quantity is the noise of the 1 kΩ metal film resistor. The plot
showing the noise power spectral density of the metal resistor after the setup noise has
been subtracted is shown in Figure 3-22 compared with the fundamental thermal noise of
the 1 kΩ resistor. This plot shows that when the setup noise is subtracted from the total
output noise, the noise obtained using Equation 3-4 overlaps with the theoretical thermal
noise predicted by Johnson [20] as illustrated in Figure 3-22.
42
1.E-13
2
Sv (V /Hz)
1.E-14
1 kΩ metal film
with setup
1.E-15
Setup noise
1.E-16
1.E-17
1.E+00
1.E+01
1.E+02
1.E+03
Frequency (Hz)
1.E+04
1.E+05
Figure 3-21. Voltage noise PSD of a 1-kΩ metal film resistor without the subtraction of
the equipment setup noise.
1E-13
2
Sv(V /Hz)
1E-14
1 kΩ metal film
with setup
noise
1E-15
1 kΩ metal film
without setup
noise
1E-16
Thermal noise
1E-17
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-22. Noise of the metal resistor with setup noise subtracted.
Noise Figure
The noise figure is a qualitative measure of the contribution of the amplifier noise
compared to the device under test noise for a measured signal. If the noise figure is low,
this implies that the Johnson noise of the source (device under test) dominates the output
noise; however, if the noise figure is large then the amplifier noise dominates the output
noise. The noise figure is expressed in term of voltage as shown in Equation 3-5 in dB.
⎛ S
⎞
NF = 20 log10 ⎜ Vout ⎟
⎝ SVsource ⎠
[ dB ]
(3-5)
43
where SVout is the voltage output noise and SVsource the voltage thermal noise source both
with units Vrms/Hz1/2. Similarly, it can be computed in terms of noise power.
⎛ S
⎞
NF = 10 log10 ⎜ Pout ⎟
⎝ S Psource ⎠
[ dB ]
(3-6)
where SPout is the noise output power and SPsource the thermal noise source both expressed
Vrms2/Hz. Equation 3-7 shown below gives the noise figure derived from the
experimental setup shown in Figure 3-18.
⎛ Total input noise power , including source noise ⎞
NF = 10 log10 ⎜
⎟
Noise power of source noise
⎝
⎠
⎛ 4 K B RdutT ∆f + Sva + Sia ( Rdut // Rin )2 ⎞
= 10 log10 ⎜
⎟
⎜
⎟
4 K B RdutT ∆
⎝
⎠
(3-7)
⎛ S + Sia ( Rdut // Rin )2 ⎞
= 10 log10 ⎜1 + va
⎟
⎟
⎜
4
K
R
T
∆
B dut
⎠
⎝
[ dB ]
The noise figure, shown in Figure 3-23, of 1 kΩ metal film resistor has been
computed to determine when the output noise is dominated by the Johnson noise of the
microphone or by the amplifier noise. From Figure 3-23, the noise figure at 1 kHz is
about 3 dB.
Noise Figure (dB)
1.E+01
1.E+00
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 3-23. Noise figure of 1 kΩ metal film resistor using the SR560 low noise
preamplifier.
44
This means that the contribution of the amplifier noise to the noise measured is
small. Thus, for devices of about 1 kΩ or higher, the noise measured will not be
dominated by the amplifier noise. Therefore, we will be able to measure their noise floor.
CHAPTER 4
MICROPHONES NOISE MEASUREMENT
In this chapter, we measure the noise power spectral densities of four microphones:
UF piezoresistive microphone [15, 16], UF proximity sensor [17], Endevco piezoresistive
microphone (8510B-1) and Kulite piezoresistive microphone (MIC–093). Using the
procedure outlined in Chapter 3, the setup noise will be subtracted from the resulting total
power spectral density of each of the measurements, and the Hooge parameter α will be
computed for the UF piezoresistive microphone and the UF proximity sensor.
First, the noise power spectral densities of the Kulite, Endevco, UF piezoresistive,
and UF proximity microphone were measured at zero bias. The measured input and
output impedances of the microphones are shown on Table 4-1.
Table 4-1. Our measured input and output impedances of UF piezoresistive microphone,
UF proximity, Kulite and Endevco
Microphones
UF
UF Proximity
Kulite
Endevco
Rin (Ω)
578
9623
3102
2057
Rout (Ω)
579
9634
1148
1820
Figure 4-1 shows the power spectral densities of UF piezoresistive microphone,
Proximity, Kulite and Endevco without the setup noise and their corresponding
theoretical thermal noise.
In Figure 4-1, we observe that the higher the resistance of the device, the higher
the PSD noise floor. This is because the observed asymptotic noise floor is due to the
thermal noise corresponding to the output impedance of the microphones and is
proportional to the resistance value.
45
46
1E-13
1E-15
2
Sv (V /Hz)
1E-14
Thermal noise
UF Proximity
1E-16
Endevco
Kulite
1E-17
1E-18
1.E+00
UF Piezoresistive
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figures 4-1. PSD of Kulite, Endevco, UF piezoresistive and UF Proximity sensor at 0
Volt without setup noise.
When the microphone is unbiased, the observed 1/f noise characteristic at low
frequencies originates from the pre-amplifier. The noise figures of the microphones are
plotted in Figure 4-2.
Noise Figure (dB)
1.E+02
1.E+01
UF Piezoresistive
Kulite
Endevco
1.E+00
UF Proximity
1.E-01
1.E-02
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 4-2. Noise figure of UF piezoresistive microphone, Kulite, Endevco, and UF
proximity sensor using the SR560 low noise pre-amplifier.
As expected, the noise figure is lowest for the proximity sensor due to its highest
output impedance of the four microphones investigated. Since the UF ultrasonic
proximity sensor has the highest output resistance and the UF microphone the lowest
47
output resistance, their noise figures are respectively the lowest and highest in Figure 4-2.
However, one should not design a device with large resistance to compete with the noise
figure because even if the noise figure is smaller the downfall is that it is achieved by
having a large thermal noise produced by the source. This high thermal noise may affect
the signal-to-noise ratio.
Since we are interested in investigating the transducer noise at frequencies below
the human hearing range to capture and characterize the low frequency 1/f component,
we will investigate the noise at frequencies starting from 0.01 Hz. Table 4.2 shows the
frequency spans of the measurements. The data have been overlapped to obtain the
power spectral density.
Table 4-2. Frequency range during measurement
Span (Hz)
FFT lines
Binwidth (Hz)
12.5
800
0.016
200
800
0.25
1600
800
2
12800
800
16
Prior to the measurement, we investigated the effect of the bias resistor (metal
film resistor) on the output resistance of the microphone, Req. The large signal and small
signal circuits are shown in Figure 4-3 and Figure 4-4.
Rbias
R1
R2
Vbias
Pre-amplifier
R4
R3
Figure 4-3. Large signal representation of bias network.
48
In small signal analysis, the voltage source becomes a short as illustrated in
Figure 4-4.
Figure 4-4. Small signal representation of bias network.
The equivalent resistance seen by the pre-amplifier is found from the circuit
above using a ∆-Υ transformation. The resulting circuit is shown in Figure 4-5.
a
R1
Rea
Rec
b
e
R4
c
Red
d
Req
Figure 4-5. Small signal representation of bias network using a ∆-Υ transformation.
The expression of the equivalent resistance seen by the pre-amplifier is given in
Equation 4-1.
Req = ( Rbae // Rbde ) + Rec = ⎡⎣( R1 + Rea ) // ( R2 + Red ) ⎤⎦ + Rec
where
(4-1)
49
Rbae =R1 + Rea
Rbde = R4 +Red
R ea = ( Rac ∗ Rad ) ( Rac + Rcd + Rad )
R ec = ( Rca ∗ Rcd ) ( Rac + Rcd + Rad )
R ed = ( Rda ∗ Rdc ) ( Rac + Rcd + Rad )
By simulating cases of balanced and unbalanced Wheatstone bridge, we found
that Rbias has no effect on the impedance seen by the amplifier when the Wheatstone
bridge is balanced. We will use this result in our analysis. The noise power spectral
density of the UF piezoresistive microphone, UF proximity, and Endevco piezoresistive
sensors will be evaluated using the setup developed in Chapter 3 and shown in
Figure 4-6.
Shielded Box
Shielded Box
Shielded Box
Rbias
A
Pre-Amp
(SR560)
Vbias
A Spectrum Analyzer
(SR785)
Chassis
B
Computer
(LabView)
AC Out
AC Out
Figure 4-6. Experimental setup of noise measurement.
However, for the Kulite piezoresistive microphone, instead of a DC bias voltage,
we use an AC bias voltage. At DC bias voltage, we were unable to observe the low
frequency noise of the Kulite microphone. This is due to the fact that the amplifier noise
dominates at low frequencies, and therefore prevented the noise measurement of the
50
Kulite under DC bias voltage. To overcome this impediment, the microphone is biased
with an AC bias voltage. The advantage of using an AC bias voltage is its capability to
modulate the microphone low frequency noise to a frequency higher that the corner
frequency of the pre-amplifier where it can be detected and measured. Figure 4-7 shows
the setup for an AC bridge measurement.
Shielded Box
Shielded Box
Shielded Box
Microphone
R1
SRS 785
R2
A
SRS 560
Spectrum
Analyzer
Amp
VAC
R3
Sv (V 2/Hz)
S v (V2/Hz)
fc-fn f c fc+fn
∆V =
=
=
Vi
Rs
Vc
Rs
Vc
Rs
B
∆R =
Vc
Rs
f (Hz)
Sv (V 2/Hz)
R4
fc-fn f c fc+fn
f (Hz)
Delta f (Hz)
fn
cos ( 2π f c t ) ∆R
∞
∑ cos ( 2π f t ) {a
c
n
cos ( 2π f n t + ϕ n )}
c
+ f n ) t + ϕ n } + cos {2π ( f c − f n ) t − ϕ n }]
n =0
∞
f0
an
∑ 2 [cos {2π ( f
⎛ ∆V ⎞
⎜
⎟
⎝ V ⎠
2
⎛ ∆R ⎞
⎟
⎝ R ⎠
2
.
= ⎜
f c +∆f
f c + ∆f
n =0
Figure 4-7. Experimental setup for an AC bridge measurement. The mathematical
derivations have been obtained from Lorteije and Hoppenbrouwers [30].
Lorteije and Hoppenbrouwers [30] describe the low frequency noise measurement
using an AC signal. They show that an AC signal with carrier frequency fc, the noise
power spectral density at frequencies fc –fn and fc +fn, where fn is a frequency component
of the fluctuating resistance, is equal to the noise power spectral density at fn for a DC
51
bias voltage. Thus, Lorteije and Hoppenbrouwers call the noise power spectral density
resulting from an AC bias voltage 1/∆f noise. Furthermore, Lorteije and
Hoppenbrouwers, through experimental result on carbon-impregnated paper, under DC
and AC bias voltages, have suggested that the noise power spectral density obtained
when an AC signal is used as bias voltage is four times smaller than the noise power
spectral density when a DC voltage is used. Therefore, one must multiply the low
frequency AC measurement by four to obtain the noise measurement for DC bias voltage.
Noise in Microphones
UF Piezoresistive Microphone
The piezoresistive microphone has been described in Chapter 2. Its voltage noise
power spectral density is measured using the setup of Figure 4-6.
1.E-12
2.68 V
2
Sv (V /Hz)
1.E-13
1.75 V
1.E-14
0.87 V
1.E-15
1.E-16
1.E-17
Thermal noise
1.E-18
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 4-8. Power spectral density of UF piezoresistive microphone at different bias
voltages.
One can observe that at high frequencies the noise power spectral density overlaps
with the Johnson noise, after extracting the setup noise. The corner frequency where the
thermal noise starts to dominate is around 1x104 Hz. The frequency range over which the
1/f noise dominates is very large. This will have a negative effect on the signal-to-noise
52
ratio not only because of the wide range over which the 1/f noise is present but also the
high noise level at low frequencies. The signal-to-noise ratio expresses the signal
strength with respect to the noise present in the system as given in Equation 4-2,
⎛V ⎞
SNR = 20 log ⎜ s ⎟
⎝ Vn ⎠
(4-2)
where Vs is the signal and Vn is the noise level.
The total RMS noise in a bandwidth, ∆f, is obtained by taking the square root of the
power spectral density integrated over the bandwidth. The noise level can be large at low
frequency because the 1/f noise increases as the frequency decreases. Equation 4-3 gives
the RMS noise voltage when two dominant noise sources in piezoresistive sensors, 1/f
and thermal noise, are considered.
Vn = 4 K B R T BW +
⎛ f ⎞
ln ⎜ 2 ⎟
N
⎝ f1 ⎠
αV 2
(4-3)
where f1 is the lowest and f2 is the highest frequencies and BW, the difference between f2
and f1, is the bandwidth. When f2 is much larger than f1, the bandwidth can be
approximated as f2. To show the voltage square dependence of the noise power spectral
density as formulated by Hooge [21], the power spectral density is plotted versus voltage
at a specific frequency in Figure 4-9. The noise voltage power spectral density values
used in this graph are taken at 12 Hz. A power regression of the data gives a voltage
dependence of 1.85 ± 0.60. The Hooge parameter α is computed to evaluate the process
quality of the piezoresistor transducer in the piezoresistive microphone since the lower
the value of α, the lower the noise, and the better the process quality. From Equation 2-5
we obtain the expression for the Hooge parameter α as shown in Equation 4-4.
53
α=
SV ∗ N ∗ f
V2
(4-4)
where Sv is the noise voltage power spectral density, N is the number of carriers, f is the
frequency at which the Hooge parameter is computed, and V is the bias voltage applied to
the microphone.
2
Sv (V /Hz)
1.E-13
-15
1.85±0.60
Sv = 1.99*10 X
1.E-14
1.E-15
1.E-01
1.E+00
1.E+01
Voltage (V)
Figure 4-9. Voltage dependence of PSD for UF piezoresistive microphone at 12 Hz and
binwidth 0.016 Hz.
The plot of the Hooge parameter is shown in Figure 4-10.
Hooge parameter Magnitude
1.E-02
1.E-03
5.E-01
2.E+00
Voltage (V)
4.E+00
Figure 4-10. Hooge parameter of UF piezoresistive microphone.
The Hooge parameter when biased at 2.68 V is estimated to be 2.9x10-03 with an
uncertainty of 2.78 %. The uncertainty was computed by applying the uncertainty
54
analysis techniques from Coleman and Steele [31] on the governing equation of the low
frequency noise power spectral density described in Equation 4-4. The Hooge parameter
value is large. It reflects the high 1/f noise levels seen in Figure 4-8. To obtain a lower
Hooge parameter, a better process quality is required.
UF Proximity Sensor
The power spectral densities of the UF proximity sensor are measured with the
same equipments and settings as the UF piezoresistive microphone. However, a bias is
applied to the substrate for junction isolation. The substrate is biased at 6.71, 4.99, and
3.15 Volts when the sensor is biased respectively at 6.23, 4.45, and 2.65 Volts. This
leads to a reverse bias voltage of about - 0.5 Volt that corresponds to a relative small
leakage current of 0.96 nA. The voltage noise power spectral densities of the UF
proximity sensor with different bias voltages are shown in Figure 4-11 at constant reverse
bias of -0.5 V.
1.E-12
6.23 V
4.45 V
2
Sv(V /Hz)
1.E-13
2.65 V
1.E-14
1.E-15
Thermal noise
1.E-16
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 4-11. Power spectral density of UF proximity sensor at different bias voltage
(constant reverse bias of -0.5 V).
The corner frequency is at 100 Hz. It is significantly lower than the corner
frequency of the UF piezoresistive microphone. A plot comparing the noise levels all
55
four microphones at the same bias voltage will be given later in this chapter. The voltage
dependence of the power spectral density is shown in Figure 4-12, giving a voltage power
dependence of 1.86 ± 2.67.
2
Sv (V /Hz)
1.E-13
-16
1.86±2.67
Sv = 2.96*10 X
1.E-14
1.E-15
1.E+00
1.E+01
Voltage (V)
Figure 4-12. Voltage dependence of PSD for UF proximity sensor at 12 Hz and binwidth
0.016 Hz.
We also compute and plot the Hooge parameter for the UF proximity sensor as
shown in Figure 4-13.
Hooge Parameter Magnitude
1.E-04
1.E-05
2.E+00
5.E+00
7.E+00
Voltage (V)
Figure 4-13. Hooge parameter of UF proximity sensor.
The value of the Hooge parameter of the UF proximity sensor when biased at 2.65
with a constant reverse bias of 3.15 V is 6.75x10-05 with an uncertainty of 2.78 %, which
is two orders of magnitude lower compared to the UF piezoresistive microphone. This
leads to the conclusion that the piezoresistor silicon defect density is significantly lower
56
and the process quality correspondingly higher for the UF proximity sensor than the UF
piezoresistive microphone. One key difference between the two devices is the use of a
high temperature wafer-bonding step in the UF piezoresistive microphone.
Endevco Piezoresistive Microphone
Noise measurements have also been performed on a commercial microphone;
Endevco (Model 8510B-1). Some of the microphone specifications have been provided
in Chapter 2. The noise measurements are conducted using the same conditions as the
previous microphones. The noise power spectral density obtained is shown in Figure 414.
1.E-12
6.96 V
2
Sv (V /Hz)
1.E-13
4.90 V
1.E-14
2.94 V
1.E-15
1.E-16
Thermal noise
1.E-17
1.E-18
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 4-14. Power spectral density of Endevco microphone at different bias voltage.
The corner frequency of the Endevco microphone is 1x103 Hz, which is higher
than the corner frequency of the proximity sensor but still lower than the UF
piezoresistive microphone. Its noise floor is lower than the noise floor of the UF
piezoresistive microphone and UF proximity sensor. Since we do not know the number
of carriers in the piezoresistor, we cannot compute the Hooge parameter. However, the
voltage dependence of the PSD is provided in Figure 4-15 and indicates a power
dependence of 1.48 ± 2.05.
57
1.E-15
-17
1.48±2.05
2
Sv(V /Hz)
Sv = 2.25* 10 X
1.E-16
1.E+00
1.E+01
Voltage (V)
Figure 4-15. Voltage dependence of PSD for Endevco microphone at 12 Hz and binwidth
0.016 Hz.
Kulite Piezoresistive Microphone
The noise power spectral density of the Kulite microphone without the
temperature compensation module (MIC-093) has been obtained via amplitude
modulation. The noise measurements are conducted with an AC bias voltage with
frequency of 10 kHz and different amplitudes of 1.06, 1.87 and 2.68 volt peak. The noise
power spectral density of Kulite microphone is shown on Figure 4-16 with corner
frequency at 10 Hz.
1.E-12
2.68 V
2
Sv (V /Hz)
1.E-13
1.87 V
1.E-14
1.06 V
1.E-15
1.E-16
Thermal noise
1.E-17
1.E-18
1.E-01
1.E+00
1.E+01
1.E+02
Frequency
(Hz)
Delta Frequency (Hz)
1.E+03
1.E+04
Figure 4-16. Power spectral density of Kulite microphone (without the temperature
compensation module) at different bias voltage.
58
The voltage dependence of the power spectral density provided in Figure 4-17.
indicates a power dependence of 1.59 ± 0.73.
2
Sv(V /Hz)
1.E-14
Sv = 2.17 * 10
-16
X
1.59 ±0.73
1.E-15
1.E-16
1.E+00
1.E+01
Voltage (V)
Figure 4-17. Voltage dependence of power spectral density for Kulite microphone
(without the temperature compensation module).
One can observe from Figure 4-15 that the noise power spectral density of the
Kulite is small. Figure 4-18 demonstrates that these noise levels at low frequency could
not be observed under DC bias voltages since the setup noise dominates.
1.E-12
DC setup noise
2.68 V
1.E-14
1.87 V
2
Sv (V /Hz)
1.E-13
1.E-15
1.06 V
1.E-16
1.E-17
1.E-01
1.E+00
1.E+01
1.E+02
Frequency (Hz)
1.E+03
1.E+04
Figure 4-18. Kulite noise power spectral densities compared to the DC setup noise.
A plot comparing the voltage noise PSD of the UF piezoresistive microphone, UF
proximity sensor, Endevco and Kulite microphones is provided in Figure 4-19. We
observe at low frequencies that the UF piezoresistive microphone has the higher noise
level, followed by the UF proximity sensor, the Endevco microphone and then the Kulite
microphone.
59
1.E-12
UF microphone
UF proximity sensor
Endevco microphone (8510B-1)
Kulite microphone (MIC-093)
1.E-14
2
Sv (V /Hz)
1.E-13
1.E-15
1.E-16
1.E-17
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
Frequency (Hz)
Figure 4-19. Comparison of power spectral densities of UF microphone, UF proximity
sensor, Endevco, and Kulite (without the temperature compensation
module) microphones biased at 2.6 V.
It is worth noticing that the resistance of the UF piezoresistive microphone is the
smallest among all the microphones. This graph reveals that, at low frequencies, the
noise is dominated by the 1/f noise while, at high frequencies the noise is thermal noise.
The main difference in the resistors beside their values is their types. The piezoresistors
of the UF piezoresistive microphone are dielectrically isolated and the ones of the
proximity sensor are junction isolated. The latter will incur shot noise but less 1/f noise
since it has fewer traps surrounding it. The 1/f noise of the UF piezoresistive microphone
is large possibly due to traps generated during the high temperature wafer-bonding step.
The corner frequency of the UF piezoresistive microphone is also the largest
compared to the other sensors. However, at high frequencies one sees a reverse in the
magnitude of the noise. The UF piezoresistive microphone shows a lower noise since it
has the smallest output resistance. This confirms the direct relation of the thermal noise
with the output resistance value as shown previously in Equation 2-2. For further
illustration of the 1/f noise contribution, we define a 1/f noise figure by subtracting the
thermal noise power from the 1/f noise power of the device. It is represented
mathematically by Equation 4-5.
60
⎛ 1/ f noise ⎞
NF1 f = 20 log ⎜
⎟
⎝ thermal noise ⎠
(4-5)
This 1/f noise figure is different than the noise figure presented in Figure 3-23 and
4-2 where the device was not biased. The quantity plotted is the difference of the total
measured noise power and the thermal noise power of the device. In Figure 2-20, we plot
the 1/f noise figure for all four sensors biased at 2.6 V.
1/f Noise Figure (dB)
100
UF microphone
UF proximity
Endevco microphone (8510-B)
10
Kulite microphone (MIC-093)
1
0.1
0
25
50
75
100
Frequency (Hz)
Figure 4-20. 1/f noise figure of UF piezoresistive microphone, UF proximity sensor,
Endevco, and Kulite (without the temperature compensation module)
microphones biased at 2.6 V.
From this plot one can see that for the sensors with higher noise voltage power
spectral densities, their 1/f noise figures dominate at the low frequency range. It is worth
noticing that, as the frequency gets larger, the 1/f noise figure of all the sensors will tend
to zero. This is expected since beyond the corner frequency, the noise is essentially the
thermal noise of the sensor.
Acoustic Calibration
In this section, we investigate the performance of the UF piezoresistive
microphone, UF proximity, Endevco, and Kulite microphones through acoustic
calibration. For the latter, the acoustic calibration is performed with and without its
temperature compensation module (TCM). The parameters measured frequency response
61
and linearity of the microphones are used to compute the sensitivity and minimum
detectable signal of the microphones.
Frequency Response
The calibration of the dynamic response of the UF piezoresistive microphone, UF
proximity, Endevco and Kulite is performed with the use of a plane wave tube. A
diagram illustrating the setup is shown in Figure 4-21.
B&K MIC
DC
Supply
DUT
Diff.
Amp
Amp
PULSE
MultiAnalyzer
Computer
(LabShop)
Figure 4-21. Experimental setup used with the normal incidence plane wave tube.
The microphones are mounted in the same plane at the end of the plane wave tube
next to a 1/8-inch Bruel and Kjaer (4138 B&K condenser microphone) integrated with a
B&K 2670 preamplifier. This setup allows both microphones to sense the same incident
pressure. The plane wave tube with a cutoff frequency of 6.7 KHz is 96 cm long, with a
2.54 cm x 2.54 cm square duct. The formation of a standing wave is generated by a JBL
2126-J compression driver mounted at the other end of the tube. The microphones are
biased using a Hewlett Packard E3630A DC power supply. The voltage settings are
specified by the manufacturers to avoid damaging the microphones. The Kulite and the
62
Endevco microphones are biased at 10 volt; the UF proximity sensor at 9 volt with a 10.5
volt reverse bias on the substrate for junction isolation and the UF piezoresistive
microphone at 3 volt. As for the B&K microphone, it is powered by a B&K PULSE
multi-analyzer system. The outputs of the microphones are connected to a low noise
amplifier, Standford Research System (SRS 560), in a differential mode. The gain of the
low noise amplifer is set to 200 and its output connected to the B&K PULSE multianalyzer system, which processes the data via LabShop software. Prior to each
microphone calibration, the B&K microphone is calibrated using a B&K 4228
pistonphone. During this measurement, a periodic random signal, supplied by a B&K
PULSE multi-analyzer system and amplified by a Techron 7540 power amplifier to drive
the speaker, is used. Also 800 FFT lines, 8000 averages, a span of 6.4 KHz, with center
frequency 3.5 KHz, resulting in a maximum frequency of 6.7 KHz are used.
Both normalized magnitude and phase frequency response of the microphones are
shown in Figures 4-22 and 4-23.
Sensitivity(uV/Pa*V)
3
Endevco
2
Kulite without TCM
UF proximity sensor
UF piezoresitive
Kulite with TCM
0
1000
2000
3000
4000
5000
Frequency (Hz)
6000
7000
Figure 4-22. Magnitude frequency response (normalized sensitivity) of Endevco, UF
proximity, Kulite (with and without the temperature compensation module)
and UF piezoresistive microphone.
63
UF piezoresitive
5
Endevco
Phase (Degree)
UF proximity
Kulite with TCM
Kulite without TCM
0
-5
1000
2000
3000
4000
5000
Frequency (Hz)
6000
7000
Figure 4-23. Phase frequency response of Endevco, UF proximity, Kulite (with and
without the temperature compensation module) and UF piezoresistive
microphone.
Linearity
The setup for the linearity measurement is the same as above. However, in this
case a 1 kHz sine wave source signal is used. The amplitude of the source signal is
progressively increased and the pressure sensed by the microphone. The corresponding
microphone output voltages are recorded until one sees a non-linear trend in the signal.
Figure 4-24 shows the linearity plots of the Endevco, proximity, UF piezoresistive
microphone and Kulite sensors up to 1500 Pa.
Sensor Outpu (uVrms)
40000
Endevco
30000
20000
Kulite
without TCM
10000
UF proximity
Kulite with TCM
UF piezoresistive
0
0
200
400
600
800
1000
Pressure ( Parms)
1200
1400
1600
Figure 4-24. Linearity measurement of Endevco, proximity, Kulite (with and without the
temperature compensation module) and UF piezoresistive microphone.
64
One observes that all the sensors exhibit linear responses up to 1500 Pa. The static
sensitivity of the microphone is obtained by computing the slope of the linearity plots.
However, another plot that one can explore is the plot of sensitivity versus the applied
pressure to better visualize the linear response of the microphones to normal incident
pressure. Such a plot is shown on Figure 4-25 for UF piezoresistive microphone
piezoresistive, UF proximity sensor, Endevco and Kulite microphones.
3
Sensitivity (uV/Pa*V)
Endevco
2
Kulite without TCM
1
UF proximity
UF piezoresistive
Kulite withTCM
0
0
200
400
600
800
1000
Pressure (Parms )
1200
1400
1600
Figure 4-25. Sensitivity of Endevco, UF proximity, Kulite (with and without the
temperature compensation module) and UF piezoresistive as a function of
pressure.
Table 4.3 summarizes the acoustic calibration of the microphones.
Table 4-3. Acoustic calibration results of UF microphone, UF proximity, Endevco and
Kulite microphones
Parameters
UF
UF
Endevco Kulite Kulite
without
microphone proximity
with
TCM* TCM*
Excitation Voltage (V)
3
9
10
10
10
Input impedance (Ω)
578
9623
2057
3102
1148
Output impedance (Ω)
579
9634
1820
1148
1148
Sensitivity (µV/Pa)
1.69
6.40
26.9
4.23
11.6
Normalized Sensitivity
0.56
0.71
2.69
0.42
1.16
(µV/Pa*V)
Measured up to
158
158
158
158
158
(dB SPL)
*TCM (temperature compensation module).
65
In Table 4-3, the excitation voltages during the microphone sensitivity
measurement are different. For a comparison point of view, it would be interesting to
measure the microphone sensitivity under identical bias condition and power dissipation.
In Table 4-4 and 4-5, we show the sensitivity of the UF microphone, UF proximity,
Endevco, and Kulite microphones under the same bias voltage (3 V) and under the same
power dissipation (7 mW).
Table 4-4. Sensitivity of the UF microphone, UF proximity, Endevco and Kulite
microphones under the same bias voltage (3 V)
Parameters
UF
UF
Endevco Kulite Kulite
without
microphone proximity
with
TCM
TCM
Sensitivity (µV/Pa)
1.69
2.32
8.60
1.26
3.40
Normalized Sensitivity 0.56
0.77
2.86
0.42
1.13
(µV/Pa*V)
Table 4-5. Sensitivity of the UF microphone, UF proximity, Endevco and Kulite
microphones under same power dissipation (7 mW)
Parameters
UF
UF
Endevco Kulite Kulite
without
microphone proximity
with
TCM
TCM
Excitation Voltage (V) 2.00
8.16
3.77
4.63
2.82
Sensitivity (µV/Pa)
1.39
6.32
10.9
1.95
3.17
Normalized Sensitivity 0.69
0.77
2.89
0.42
1.12
(µV/Pa*V)
From Table 4-4, when all microphones are biased at 3 V, we observe a larger
sensitivity from Endevco, followed by Kulite without TCM, UF proximity, UF
piezoresistive microphone and Kulite with TCM. When the sensors are subjected to the
same power dissipation (7 mW), as shown in Table 4-5, a larger sensitivity is observed
from Endevco, followed by UF proximity, Kulite without TCM, Kulite with TCM and
UF piezoresistive microphone. The UF piezoresistive is biased at 2 V. If it was biased at
3 V, then the UF proximity would have been biased at 12.24 V in order to have the same
power dissipation in both sensors. However, 12.24 V is larger than the maximum bias
66
voltage applicable to the UF proximity sensor (10 V). A power dissipation of 7 mW
allows us to bias the UF proximity sensor without exceeding its maximum bias
constraint.
Minimum Detectable Signal
The minimum detectable signals are shown in Table 4-6 for UF piezoresistive
microphone, UF proximity, Endevco and Kulite. They are computed in a binwidth of 2
Hz centered at 1 kHz with the microphone biased at different bias voltages as shown in
Table 4-3. The minimum detectable signal is the ratio of the noise voltage to the
sensitivity. It is expressed as shown in Equation 4-6.
MDS =
Noise voltage
Sensitivity
(4-6)
Table 4-6. Minimum detectable signal (MDS) of UF microphone, UF proximity,
Endevco and Kulite microphones at different bias voltages
Parameters
UF
microphone
UF
proximity
Excitation Voltage (V)
MDS for 2 Hz bin
centered at 1 kHz (SPL)
3
51.5
9
43.2
Endevco Kulite
With
TCM
10
10
23.8
38.1
Kulite
Without
TCM
10
29.3
In Table 4-6, the Endevco has the lowest MDS followed by the Kulite, the UF
piezoresistive microphone and the proximity sensor.
The minimum detectable signals when the microphones are operated under the
same bias voltage (3 V) and same power dissipation (7 mW) are shown respectively in
Table 4-7 and 4-8.
From Table 4-7, when all microphones are biased at 3 V, we observe a lower MDS
from Endevco, followed by Kulite without TCM, Kulite with TCM, UF piezoresistive
microphone and UF proximity.
67
Table 4-7. Minimum detectable signals (MDS) when the microphones are operated
under the same bias voltage (3 V)
Parameters
UF
UF
Endevco Kulite Kulite
Without
microphone proximity
with
TCM
TCM
Excitation Voltage (V)
3
3
3
3
3
MDS for 2 Hz bin centered 51.5
51.8
33.4
48.6
40.0
at 1 kHz (SPL)
Table 4-8. Minimum detectable signals (MDS) when the microphones are subjected to
the same power dissipation (7 mW)
Parameters
UF
UF
Endevco Kulite Kulite
Without
microphone proximity
with
TCM
TCM
Excitation Voltage (V)
2.00
8.16
3.77
4.63
2.82
Power Dissipation (mW)
7
7
7
7
7
MDS for 2 Hz bin centered 53.2
43.1
31.3
44.8
40.6
at 1 kHz (SPL)
When the sensors are subjected to the same power dissipation (7mW), as shown
in Table 4-8, a lower MDS is observed from Endevco, followed by Kulite without TCM,
UF proximity, Kulite with TCM, and UF piezoresistive microphone.
Dominant Noise Source in MEMS Piezoresistive Microphones
The theory of the existence of a purely mechanical 1/f noise dominant at low
frequency has been suggested by Zuckerwar et al. [4]. In this section, we demonstrate
that the 1/f noise at low frequencies is electrical by nature and is dominant.
Acoustic Isolation Test
The noise measurement is performed in a Faraday cage. The purpose of the
acoustic isolation test is to quantify the acoustic sound pressure in the Faraday cage using
a sensitive B&K microphone (1/8-inch Bruel and Kjaer 4138 condenser microphone).
This result reveals whether the experiment is acoustically shielded. The coherence
between a calibrated Bruel and Kjaer 4138 condenser microphone and the UF
piezoresistive microphone help us to see if there is an acoustic deterministic source of the
68
measured electrical noise, i.e. the acoustic analog of EMI. Figure 4-26 shows the power
spectral density of the Bruel and Kjaer 4138 condenser microphone and of the UF
2
Spa (Pa /Hz)
piezoresistive microphone.
1.E+00
UF piezoresistive microphone (Vbias = 3 V)
1.E-01
B&K
1.E-02
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
1.E-10
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
Frequency (Hz)
Figure 4-26. Power spectral density of the Bruel and Kjaer 4138 condenser microphone
and of the UF piezoresistive microphone.
We observe from Figure 4-26 that a low level acoustic signal is present inside the
Faraday cage during the electrical noise measurement. Although, the acoustic isolation
of our setup is not as good as the one of Zuckerwar et al. [12], the acoustic signal is much
smaller than the equivalent signal of the UF piezoresistive microphone. Figure 4-27
shows the coherence function between the B&K and UF piezoresistive microphone.
1.00
Coherence
0.80
0.60
0.40
0.20
0.00
0
1
10
100
1000
10000
Freque ncy (Hz)
Figure 4-27. Coherence function between the B&K and UF piezoresistive microphone.
69
From the above figure, note that the coherence between the acoustic signal and
the electrical noise is small for most frequencies. An exception occurs at 60 Hz. At that
particular frequency, the coherence is larger and has a value close to 0.6. This coherence
value at 60 Hz may be due to a common 60 Hz electrical contamination. Therefore, one
may conclude that the acoustic interference contribution to the measured electrical noise
is negligible. Having quantified the impact of the acoustic signal in our measurement, we
will now see whether the origin of the 1/f noise is mechanical or electrical in nature.
Membrane Contribution to 1/f Noise
To investigate whether the dominant source of the 1/f noise is mechanical or
electrical of origin, we perform power spectral density measurement on two UF
piezoresistive proximity sensors of identical structures except that one has a free
membrane and the other has fixed membrane.
1.E-12
1.E-13
2
Sv (V /Hz)
UF piezoresistive proximity
with released membrane
8V
5V
1.E-14
1.E-15
0V
1.E-16
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
piezoresistors
free
n-Si
Figure 4-28. Power spectral density of the UF piezoresistive proximity sensor with free
diaphragm.
70
If the noise is mechanical of origin, then whether the sensors are biased or not, a 1/f
noise characteristic must be present on the microphone with free membrane since the
damping resistance, Ra, of the microphone diagram is related to the purely mechanical 1/f
noise [4, 12].
Figure 4-28 shows the power spectral density of the UF piezoresistive proximity
sensor with free diaphragm. Figure 4-29 shows the power spectral density of the UF
piezoresistive proximity sensor with fixed diaphragm.
1.E-12
UF piezoresistive proximity
with unreleased membrane
8V
2
Sv (V /Hz)
1.E-13
5V
1.E-14
1.E-15
0V
1.E-16
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
piezoresistors
fixed
n-Si
Figure 4-29. Power spectral density of the UF piezoresistive proximity sensor with fixed
diaphragm.
Comparing Figures 4.28 and 4.29, we observe that excess noise is present in both
mechanically fixed and free diaphragms. In addition, as the bias voltage increases, the
power spectral density at low frequencies increases. For the cases when the microphones
are not biased the excess noise coincides with thermal noise. In this case, the excess
71
noise as illustrated on Figure 4-30 for the sensor with free membrane corresponds to the
excess noise of the low noise pre-amplifier (SRS 560).
1.E-12
1.E-14
2
Sv (V /Hz)
1.E-13
1.E-15
0V
1.E-16
Setup noise with SR 560
1.E-17
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Frequency (Hz)
Figure 4-30. Power spectral density of UF proximity sensor with free membrane at zero
biased voltage.
A similar plot is obtained for the sensor with fixed diaphragm at zero biased zero.
On Figure 4-28 and 4-29, the setup noise has been removed. For the zero biased cases
the power spectral densities show that the low noise is mainly the amplifier low noise.
However, at frequencies higher than the corner frequency of the amplifier, the thermal
noises of the sensors dominate. We can conclude from the measurements that the
source of excess noise is electrical.
CHAPTER 5
CONCLUSION AND FUTURE WORK
We have discussed noise measurement techniques such as using Faraday cages
for shielding, lead acid battery for biasing, single point ground to avoid ground loops, and
evaluation and subtraction of setup noise. These techniques are implemented during the
noise power spectral density measurement of UF piezoresistive microphone, UF
proximity sensor, Endevco piezoresistive microphone (8510B-1) and Kulite
piezoresistive microphone (MIC-093). In addition, the settings of the low noise
amplifiers (SRS 560 and Brookdeal 5004) and spectrum analyzer (SRS 785) are
provided. Noise power spectral densities are obtained, voltage square dependent of the
1/f noise is shown, and Hooge parameters of the UF piezoresistive microphone, UF
proximity sensor are computed. Using the power spectral densities measurement and the
acoustic calibration of the microphone in a plane wave tube we have been able to
compute the minimum detectable signal of the microphones, which is a key factor for a
large the dynamic range of a MEMS sensor.
To improve the dynamic range of MEMS piezoresistive microphones one should
consider minimizing the noise. Since we have proven that the dominant noise in MEMS
piezoresistive microphone is electrical of origin, special attentions should be on
techniques to reduce the noise through new fabrication techniques of MEMS
piezoresistive microphones. Geometrical and process fabrication parameters such as
piezoresistor surface to volume ratio, pre-amorphization, annealing, and doping
concentration impact the design of dielectrically isolated resistors and junction isolated
72
73
resistors. In addition, the study of the correlation between defects densities and 1/f noise
enable the design of low noise process flows to fabricate low noise MEMS microphones.
Figure 5-1 shows the results of a focus ion beam (FIB) and the defects in an arc
piezoresistor of the UF piezoresistive microphone are shown using a transmission
electron microscopy (TEM) as shown in Figure 5-2.
Sample
Area
Arc
Resistor
Contact
Figure 5-1. Focus ion beam (FIB) of an arc piezoresistor of the UF piezoresistive
microphone.
Nitride
Threading
dislocation
SiO2
SiO2
Nitride
P+
Silicon
Figure 5-2. Transmission electron microscopy (TEM) results of an arc piezoresistor of
the UF piezoresistive microphone.
The combination of piezoresistor noise theory and measurements and the
optimization approach used by Papila et al. [32] have the potential to yield optimally high
performance piezoresistive microphones.
APPENDIX
PIEZORESISTIVITY
Piezoresistivity is a material property where the material resistivity changes with
applied stress. Resistivity, as described in Equation A-1, is inversely proportional to the
doping concentration n, carrier mobility µ, and electron charge q. Resistivity is related to
the applied stress through piezoresistance coefficients.
ρ=
1
[Ω − cm]
nµ q
(A-1)
Silicon, which is a crystal with cubic symmetry, has three fundamental
piezoresistive coefficients, π11, π12, and π44. Its piezoresistance coefficient matrix is
shown below in Equation A-2 [33].
0
0 ⎤ ⎡σ 1 ⎤
⎡ ∆ρ1 ⎤ ⎡π 11 π 12 π 12 0
⎢ ∆ρ ⎥ ⎢π
0
0 ⎥⎥ ⎢⎢σ 2 ⎥⎥
⎢ 2 ⎥ ⎢ 12 π 11 π 12 0
0
0 ⎥ ⎢σ 3 ⎥
1 ⎢ ∆ρ3 ⎥ ⎢π 12 π 12 π 11 0
⎢
⎥=⎢
⎥⎢ ⎥
0
0 π 44 0
0 ⎥ ⎢ τ1 ⎥
ρ ⎢ ∆ρ 4 ⎥ ⎢ 0
⎢ ∆ρ5 ⎥ ⎢ 0
0
0
0 π 44 0 ⎥ ⎢ τ 2 ⎥
⎢
⎥ ⎢
⎥⎢ ⎥
0
0
0
0 π 44 ⎥⎦ ⎢⎣ τ 3 ⎥⎦
⎢⎣ ∆ρ 6 ⎥⎦ ⎢⎣ 0
(A-2)
where σ1=σxx, σ2=σyy, and σ3=σzz are the normal stresses, and τ1=τyz, τ2=τxz, and τ3=τxy
are the shear stresses.
The piezoresistance coefficient magnitude changes with orientation. To properly
determine its value for different orientations, a coordinate transformation must be
performed [34]. The piezoresistance coefficients for n-type and p-type silicon at a
specific given resistivity are shown in Table A-1 [33].
74
75
Table A-1. Piezoresistive coefficients of silicon*
π11
π12
ρ(Ω-cm)
Silicon
-11
-1
(10 Pa )
(10-11 Pa-1)
p-type
7.8
6.6
-1.1
n-type
11.7
-102.2
53.4
*Smith [33].
π44
(10-11 Pa-1)
138.1
-13.6
The piezoresistance coefficient may be decomposed into a transverse piezoresistive
coefficient, πt and a longitudinal piezoresistive coefficient πl when the stress is
perpendicular or parallel to the electric field respectively. These transverse or
longitudinal piezoresistance coefficients are given in Equation A-3 in terms of the
piezoresistance coefficients π11, π12, π44, and the direction cosines (l,m) [34].
π t = π 12 − (π 44 + π 12 − π 11 )(l12l22 + m12 m22 + n12 n22 )
π l = π 11 + 2(π 44 + π 12 − π 11 )(l12 m12 + l12 n12 + m12 n12 )
(A-3)
The polar plots of longitudinal and transverse coefficient of piezoresistance
coefficients for p-type (100) silicon are shown in Figure A-1 using the values of π11, π12,
and π44 of Table A-1.
Figure A-1. Polar plots of longitudinal and transverse piezoresistance coefficients for ptype (100) silicon.
Observing Figure A-1, one notices that the piezoresistance coefficients are larger
in the <110> direction and that the transverse piezoresistance coefficients are
76
approximately equal but have opposite sign compared to the longitudinal piezoresistance
coefficient. This is a reason why the piezoresistors of the UF microphones are oriented in
this direction in a Wheatstone bridge circuit configuration. Using Equation A-3, the
transverse or longitudinal piezoresistance coefficients, as shown in Table A-2 along the
<110> direction on a (100) wafer for room temperature and lowly doped silicon.
Table A-2. Transverse and longitudinal piezoresistance coefficients of silicon for <110>
direction
Silicon
πl (10-11 Pa-1)
πt (10-11 Pa-1)
p-type
71.8
-66.3
n-type
-31.2
-17.6
Note for <110> p-type silicon, πl is of opposite sign and almost same magnitude as
πt, which is not the case for n-type silicon where πl and πt have neither opposite sign nor
similar magnitudes. For this reason, piezoresistors are typically oriented in the <110>
direction on p-type silicon. The piezoresistance coefficient varies inversely with doping
concentration. From Equation A-1, we observe that as the doping concentration
increases, the resistivity decreases, yielding a decrease in the resistance. Kanda [35] has
investigated the dependence of the piezoresistive coefficients on doping concentration
and temperature using Fermi-Dirac statistics. A recent study by of the doping
dependence of the π coefficient by Harley and Kenny [1] is different from Kanda’s
theoretical prediction at high concentrations. Harley and Kenny [1] fit the data obtained
from Manson et al. [36], Tufte and Stetzer [37] and Kerr and Milnes [38] and show that
at high doping concentration, the decrease of the piezoresistance coefficient is
approximated by a linear relationship.
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BIOGRAPHICAL SKETCH
Robert Dieme was born on February 28th, 1974, in Diourbel, Senegal. After
finishing high school in 1995, he received the Associate of Arts certificate from
Tallahassee Community College in December 1998. He graduated with a bachelor
degree in electrical engineering from the University of Florida in December 2001.
He then started the degree for Master of Science in electrical engineering at the
University of Florida in the spring of 2002 under the guidance of Dr. Toshikazu Nishida.
He wishes to pursue a PhD degree, concentrating in the optimization of noise in
piezoresistors.
80