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Noise in MEMS
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IOP PUBLISHING
MEASUREMENT SCIENCE AND TECHNOLOGY
Meas. Sci. Technol. 21 (2010) 012001 (22pp)
doi:10.1088/0957-0233/21/1/012001
TOPICAL REVIEW
Noise in MEMS
F Mohd-Yasin1 , D J Nagel2 and C E Korman2
1
2
Faculty of Engineering, Multimedia University, 63100 Cyberjaya, Selangor, Malaysia
Department of ECE, The George Washington University, Washington, DC 20052, USA
Received 6 August 2007, in final form 6 July 2009
Published 6 November 2009
Online at stacks.iop.org/MST/21/012001
Abstract
This review provides a comprehensive survey of noise research in MEMS. Some background
on noise and on MEMS is provided. We review noise production mechanisms, and highlight
work on the theory and modeling of noise in MEMS. Then noise measurements in the specific
types of MEMS are reviewed. Inertial MEMS (accelerometers and angular rate sensors),
pressure and acoustic sensors, optical MEMS, RF MEMS, surface acoustic wave devices, flow
sensors, and chemical and biological MEMS, as well as data storage devices and magnetic
MEMS, are reviewed. We indicate opportunities for additional experimental and
computational research on noise in MEMS.
Keywords: noise, MEMS, micro systems
actuator, which turns information into a physical, chemical or
biological effect, can be negatively impacted by noise.
The second deleterious result of noise is to degrade or
limit the output of sensors or measurement systems that turn
any of the external effects into information. Virtually all such
systems have a calibration curve, as shown schematically in
figure 1. Calibration curves relate what is being measured,
the measurand M, to the signal S from the sensor or system.
The slope S/M is the responsivity of the sensor. The
useful range is capped on the high end by saturation of some
part of the system. Noise limits how small a value of the
measurand can be detected reliably. That is, noise determines
the limit of detection (LOD), which is also called the minimum
detectable limit (MDL), of the measurand for some particular
measurement situation.
Much attention has been given to the LOD of analytical
and other measurement systems. Sometimes, the LOD is
simply taken as the value of the measurand at which the
mean signal is 3σ above the mean of the noise values. Here,
σ is the standard deviation of the distribution of the noise
values obtained over time. Alternatively, ‘receiver operating
characteristics’, called ROC curves, are employed for more
precise but more complex determination of the tradeoffs
involved in determining the LOD. ROC curves permit rational
choices of the number of false positives that can be tolerated
for a given situation and sensor system.
1. Introduction to noise
Noise is an area of science and technology that poses practical
problems but also has deep intellectual attractions. The
diverse mechanisms and magnitudes of noise challenge both
their understanding and control. There are two fundamental
and inescapable reasons for noise in electrical and other
systems. One is the quantization of basic physical entities,
such as electrons, atoms and molecules. The other is the
large numbers of such units in most situations, and the
inevitable variances in the number of entities. The energies
associated with particles, photons and other quanta also have
unavoidable distributions. Systems with small numbers of
discrete units can be handled deterministically. Other systems
with large numbers of discrete units, such as vehicular traffic,
are intermediate between deterministic and statistical. But
electronic and other systems have such large numbers of quanta
that only statistical treatments are tenable for manageable
description of device behavior.
Noise includes both unavoidable noise intrinsic to
the system being used and extrinsic noise that might be
ameliorated by shielding or other means. The problems caused
by noise are well known. They fall into two categories. The
first is degradation of performance. The decline in fidelity
of the output of an acoustic system, such as a speaker, is a
familiar example. In general, the quality of the output of any
0957-0233/10/012001+22$30.00
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© 2010 IOP Publishing Ltd Printed in the UK
Meas. Sci. Technol. 21 (2010) 012001
Topical Review
numbers of journals and conferences have been dedicated to
this particular field. Various reference books are dedicated to
this topic (Korvink and Greiner 2002, Maluf 1999, Senturia
2000, Kovacs 1998, Rebeiz 2002a, Pelesko and Bernstein
2002, El-Haks 2001, Santos 2002). Moreover, patents on
MEMS are now granted at a global rate exceeding one per
work-day.
Δ
Δ
3. Overview of this review
Figure 1. Left: schematic of a calibration curve for a sensor or an
analytical instrument. Calibration curves need not be linear over
their dynamic ranges, as shown here. Both axes can be either linear
or logarithmic. Right: schematic of the control curve for an
actuator. Control curves are often nonlinear and sometimes
hysteretic, in which case the output for a given input can be double
valued. The axes for control curves of actuators are generally linear.
In general, the role of noise in MEMS has two aspects, similar
to noise in any devices. The first is the existence of various
noise sources, while the second is the practical limitations
that noise places on a MEMS system. Due to the diversity
of MEMS, there are many noise sources, depending on the
physical and other characteristics of the sensors and actuators.
For example, the noise sources in a mechanical system can be
different than the noise sources in optical, magnetic or fluidic
systems. Moreover, most micro systems involve two or more
physical or other characteristics, such as optical MEMS, which
have electrical, mechanical and optical mechanisms, all tightly
integrated.
It is well known that noise is the limiting performance
factor in many systems. Before the introduction of MEMS,
there was less need to closely examine the influence of noise for
many devices, because vibration or other instabilities generally
came from external sources (Talghader 2004). However, the
development of MEMS has changed this balance between
the extrinsic and intrinsic noise. Due to the miniaturization,
the interaction of noise energy with an extremely small mass
can cause distortion that will affect the performance of a micro
system, opening opportunities for the study of noise from new
perspectives. For example, the mechanical–thermal noise is
not a new concept, but its effects were rediscovered when
MEMS sensors were pushed to the limits of their performance.
MEMS sensors and actuators all involve some
mechanisms and associated microstructures.
Common
mechanisms are capacitive, piezoelectric, piezoresistive and
tunneling. Several types of MEMS work using alternative
mechanisms. Pressure sensors, for example, can operate
on capacitive, piezoresistive, interferometric and other
mechanisms. The noise to which the different mechanisms
are subject varies widely.
MEMS structures include
cantilevers, beams, membranes and inter-digitated (comb)
electrodes, among others. These structures also have diverse
susceptibilities to different types of noise. There is no obvious
way to categorize the subject of noise in MEMS. We chose to
organize this review by the types of MEMS devices, because
they tend to be closely coupled to the kinds of applications.
However, the different types of MEMS can have many distinct
applications. Accelerometers are a good example, since they
are used in automobiles, toys, cell phones, cameras and laptop
computers.
This review provides a comprehensive recap of mostly
experimental studies of noise in MEMS. The next section
gives some background information on noise sources. A
brief section on theory and modeling of MEMS noise follows.
Another short section on techniques for the measurement of
Noise can also limit the output of MEMS and other
actuators at low values of the input (control) signals, as shown
in figure 1. Control curves relate the electrical input, which
varies over some range, to the mechanical output, which is
full scale (FS) at 100% of the input value. For sensors, the
measurand is often stable (not noisy), although the position of
what is being measured can be noisy for mechanical sensors.
For MEMS actuators, the performance can be limited by either
electrical input or mechanical output noise.
In short, the performances of both types of transducers,
sensors and actuators of any size, can be degraded by noise.
Such problems can be especially acute for MEMS transducers
because of the relatively small sizes of these devices and their
electronic, mechanical and other parts.
2. Introduction to MEMS
MEMS sensors and actuators are devices that have static or
movable components with some dimensions on the scale of a
micrometer. Micromachined sensors and actuators commonly
combine the electronic, mechanical, optical, magnetic or other
components in a single chip (Nagel and Zaghloul 2001).
MEMS is a well-established field, which has its roots in
the 1960s and it is still evolving rapidly. Today, hundreds
of MEMS components are being used in a broad range of
applications. MEMS devices, especially sensors, are now sold
by the hundreds of millions annually. Pervasive ownership
and use of MEMS are becoming normal.
The annual revenues for MEMS sensors and actuators
are predicted by Yole Development to exceed 10 billion USD
during 2010. MEMS transducers are expected to dominate
some markets eventually due to the three advantages over
conventional sensors and actuators, namely high performance,
low cost and low power.
MEMS-based accelerometers and pressure sensors in
automotive and other industries have proven to be very
successful applications. Furthermore, RF MEMS and optical
MEMS are increasingly being adopted in telecommunication
systems. Due to these commercial successes, the research and
development of MEMS are actively being pursued around the
world, especially in the USA, Germany and Japan. Substantial
2
Meas. Sci. Technol. 21 (2010) 012001
Topical Review
noise from MEMS devices is provided next. Then, we survey
noise in some broadly useful MEMS structures. The core
of this review consists of summaries of experimental studies,
the state of the art of noise measurements, in specific types
of MEMS devices. They include accelerometers, angular
rate sensors, pressure sensors, microphones, optical MEMS,
RF MEMS, SAW devices, flow sensors, chemical sensors,
biosensors, data storage devices and magnetic MEMS. Finally,
our conclusions and recommendations are presented, one of
which deserves highlighting, namely the interactions of noise
mechanisms in micro- and nano-scale devices.
A primary challenge in simulating and designing MEMS
devices is the close coupling between electrical, mechanical,
optical and other mechanisms active in almost all MEMS
devices. It is not possible to achieve a proper MEMS
simulation or design without taking account of all the
relevant mechanisms and their influence on each other. For
example, the motion of electrons induces mechanical forces,
and deflections cause changes in charge distributions. A
fundamental question concerns the coupling of the noise
that accompanies the various physical or other mechanisms
active in any one MEMS device. That is, does the presence
of electronic noise, say Johnson (thermal) noise, influence
mechanical (Brownian) noise, which can affect the very
small masses in MEMS devices, and vice versa? Similarly,
thermal adsorption and desorption noise is mechanical on a
molecular level, but can involve electronic effects, when ions
are involved. The nature and strengths of the various possible
interactions of noise mechanisms remain open research
questions, both theoretically and experimentally.
The units with which noise in MEMS and other devices are
quantified are numerous and often relatively complex. Several
noise units were employed in the studies we review. Hence,
we provide an appendix, which surveys and discusses units for
noise.
systems has two root causes. The first is the granularity
of the energy and matter in devices. Photons, electrons,
atoms and molecules are quanta. Their existence within or
impact onto devices is unavoidably discrete. The second
reason for appearance of noise is the unavoidable statistical
variations in the energies and motions of the large numbers
of the relevant quanta. In large systems, the discrete and
statistical nature of the presence and motions of energy and
matter is often negligible. As the sizes of the systems decrease,
signals tend to decrease and subsequently, the noise tends
to increase on a relative scale. Together, this has double
impacts on the signal-to-noise ratios (SNR). Practical limits
on the minimum detection limits of MEMS sensors, and on
the minimum required input signals for MEMS actuators,
are both set by noise levels. Besides providing engineering
limits on the performance of MEMS devices, noise is a
complex intellectual subject. This is true for individual noise
mechanisms operating within a particular MEMS structure.
The subject of interactions between noise mechanisms is even
more complex, when there are multiple types of energies in
a MEMS device, usually electrical and mechanical, but also
optical, radio frequency and others.
There are discussions of many types of noise in the
following sections. In the rest of this section, we provide terse
summaries of the character of several of these mechanisms.
There is one noise mechanism that cuts across most types of
MEMS, namely shot noise. It is due precisely to the quantized
character of the signals and materials in MEMS. Shot noise
is caused by the variable (random) arrival times of electrons
or photons, or the necessarily discrete motions of atoms or
molecules within or onto a MEMS device.
Electronic noise is most broadly important in MEMS
because of the inevitable electronic character of both MEMS
sensors and actuators. There are a few electronic noise
mechanisms that receive most attention.
They are as
follows.
4. Noise sources
• Thermal (Johnson or Nyquist) noise, which is due to
temperature-induced fluctuations in carrier densities (as
well as in the motions of atoms and molecules).
• Generation–recombination noise, which is caused by
random production and annihilation of electron–hole pairs
in semiconductors. It can also appear in and after the
ionization due to the absorption of energetic quanta.
• Flicker noise, which varies inversely with frequency
(1/f ), and is due to variable trapping and release of
carriers in any conductors. Different types of flicker noise
occur in diverse systems of widely varying characters and
size scales (Bak 1996).
Mechanical noises, such as microphonics and vibrations, are
commonly extrinsic. However, there is one fundamental
intrinsic mechanical noise mechanism, namely Brownian
motion. It is due to the dynamic unbalanced forces caused by
random impacts of molecules on a small particle or structure.
Hence, it is also called ‘random walk’ noise. Brownian motion
becomes more significant as the size of a structure decreases,
for example, the proof mass in a MEMS accelerometer or a
resonant beam in a MEMS RF filter. Adsorption–desorption
noise is closely related to Brownian motion. It is due to
Noise has many meanings, so it is necessary to identify the
types of noise of interest in this review. Noise in components
such as MEMS, and in systems containing them, has two
fundamental origins, one external (extrinsic) and the other
internal (intrinsic). Noise from outside of MEMS devices
due to ambient electromagnetic fields or mechanical motions,
notably sound and vibration, can limit the performance of a
system. However, external noise sources are not within the
scope of this review. The magnitude of external noise signals
coupled into a MEMS device varies with the local conditions,
that is, the ambient electronic and mechanical environment,
and it also depends on the packaging and mounting of the
MEMS device. Our focus is on the fundamental noise sources
within MEMS devices because they provide the hard limits
on the device performance. The reduction of intrinsic noise
from various basic mechanisms is an important challenge to
the MEMS designer.
Before enumerating some of the more widespread and
important noise sources in MEMS, it is useful to reconsider the
fundamental causes of noise, in general. Noise in engineering
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Meas. Sci. Technol. 21 (2010) 012001
Topical Review
Table 1. Papers reporting on theory and modeling of MEMS noise.
Paper
Device or structure
Focus
Characterization
Gabrielson (1993)
Accelerometers, pressure sensors,
capacitive microphones
Accelerometers, infrared thermal
detectors, micro-beams
Microcantilevers and micro-resonators
Micro bars
Resonators (micro-beams)
Gyroscopes
Mechanical–thermal noise
Theory
Several mechanisms
Theory
Several mechanisms
Mechanical noise
Several mechanisms
Mechanical–thermal noise
Theory and computations
Theory
Theory and computations
Theory
Djuric (2000)
Djuric et al (2002)
Greiner and Korvink (1998)
Vig and Kim (1999)
Leland (2005)
noise sources at the input, which would produce output noise
equal to the actual output noise. That is, the fictitious ‘input
referred noise’, multiplied by the gain of an amplifier, equals
the actual output noise. The idea is to enable a fair comparison
of the noise introduced by an amplifier. This ‘noise’ may be
due to the effects of several mechanisms in diverse components
within the amplifier. Hence, like ambient noise, it is not of
interest for this review.
This summary of the noise sources in electrical,
mechanical, optical, RF and magnetic MEMS is not
comprehensive. For example, we did not address thermal
conductance noise, which is due to fluctuations in the heat
conductivity of pixels in MEMS infrared detector arrays.
However, the more general noise sources cited above provide
backgrounds for most of the specific noise studies that are
discussed in the following sections. Next, we review briefly
some of the theoretical, analytical and computational work on
noise in MEMS.
the random arrival and departure of individual atoms and
molecules on the surface of a MEMS device. Adsorption–
desorption noise involves some non-zero particle residence
time on a surface, in contrast to the transient impacts that
cause Brownian motion. It is a common problem in chemical
and biological sensors, which contain small structures.
An important type of noise in an optical beam is noise
in its intensity. It results from quantum noise (associated
with laser gain and cavity losses), partly from sources such as
excess noise of the pump source, vibrations of cavity mirrors or
thermal fluctuations in the gain medium. The resulting relative
intensity noise (called RIN) also depends on the operation
conditions. In particular, it often becomes weaker at high
pump powers, where the relaxation–oscillations are strongly
damped.
In the RF domain, an ideal carrier would appear as an
infinitesimally thin line in a frequency spectrum. The typical
carrier, however, will have skirts whose amplitudes roughly
follow 1/f distributions for frequencies relative to and away
from that of the carrier. These skirts are the envelope of
sidebands due to modulations of the carrier, and are FM and
AM in nature, random in both frequency and amplitude, and
caused by various phenomena relating to the physics of the
particular oscillator. They are commonly referred to as phase
noise. Phase noise is typically expressed in units of dBc Hz−1
at various offsets from the carrier frequency. dBc is the noise
intensity relative to the carrier strength. Phase noise can be
measured and expressed as SSB (single sideband) or DSB
(double sideband) values.
Granularity in magnetic media produces zigzag transitions
of their magnetic polarizations. The exact locations of the
zigzags change from one secondary action to the next. This
causes media noise (also known as transition noise or zigzag
noise). It has become the dominant noise source in modern
disk drive channels.
It must be noted that presenting and discussing the many
equations that relate the amount of each type of noise to the
governing parameters, especially temperature, are beyond the
scope of this review. The authors refer readers to the works of
Gabrielson (1993), Djuric (2000), Kulah et al (2006), Yeh and
Najafi (1997a, 1997b), Seshia et al (2002a, 2002b) and Cleland
and Roukes (2002). These papers contain the expressions for
computing the magnitude of contributions from various noise
mechanisms in several MEMS devices.
In reading papers on noise, one encounters the concept
called ‘input referred noise’. It refers to representing the
effect of all of the noise sources in an amplifier circuit by
5. Theory and modeling
Substantial work has been done on the theory and modeling
of MEMS noise. Table 1 is a summary of the selected works
being highlighted in this review. The most notable work is
by Gabrielson (1993), who published a paper that discussed
the effects of mechanical–thermal noise for MEMS, which
is the basis of much subsequent work. He reviewed several
techniques for calculating the mechanical–thermal noise in
simple MEMS structures, such as a mass-spring accelerometer,
pressure sensor, capacitive microphone and electron tunneling
accelerometer. In this 1993 paper, Gabrielson used Nyquist’s
relation to give the spectral density of the fluctuating force
related to any mechanical resistance, which is a direct physical
analog of Johnson noise for electrical resistance. It is given in
the equation
Fmechanical−thermal noise = 4kB T R,
(1)
where kB is the Boltzmann constant, T is the absolute
temperature and R is the mechanical resistance, most
commonly known as a damping coefficient.
To date,
Gabrielson’s paper had been cited more than 300 times. It
remains as the most referenced paper on noise in MEMS.
One follow-up study was performed by Djuric (2000)
who derived more complex noise models. He combined
mechanical–thermal noise with electrical noise sources, such
as shot noise, thermal noise and 1/f noise in the improved
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Meas. Sci. Technol. 21 (2010) 012001
Topical Review
Figure 2. Schematic diagram for a MEMS accelerometer with a differential capacitance as the means of detecting motion of the proof mass
relative to the frame (gray). A simple capacitance bridge is used to detect the motion-induced capacitance differential between C1 and C2. A
force feedback unit, consisting of two capacitors (CF1 and CF2), holds the mass near its undeflected position in order to broaden the dynamic
range (voltages on CF1 and CF2 are not shown). Mechanical noise can affect the mass and electronic noise the circuit (after Djuric 2000).
model. The equations for some of the most common electrical
noise sources are given below:
√
Vthermal noise = 4kT BR,
(2)
become smaller. It was observed that, with decreasing
dimensions, the relative instabilities increased, which caused
devices to fluctuate. Further investigation revealed that
the fluctuations were caused by temperature, adsorption–
desorption of molecules, out gassing, Brownian motion, drive
power, self-heating and random vibration. The authors derived
the equation for the noise of micro- and nano-resonators due
to temperature fluctuations.
Another theoretical work on noise in MEMS focused on
the micro gyroscope (angular rate sensor). Leland (2005)
derived expressions for the effect of mechanical–thermal noise
on a vibrational gyroscope, including the angular random walk,
the noise-equivalent rotation rate and the spectral density of
the noise component of the rate measurement. He calculated
and compared the output due to rotation and the output due to
noise, using stochastic averaging to obtain an approximate
‘slow’ system. The paper clarifies the impact of thermal
noise and shows the effect of a frequency mismatch between
the drive and sense axes. The noise-equivalent rates for both
open-loop and force-to-rebalance operation of the gyroscope
were also found.
where B is the measurement bandwidth and R is the electrical
resistance;
Ishot noise = 2qIdc B
(3)
where q is the electron charge (1.6 × 10−19 coulomb), Idc is
the average direct current (A) and B is the noise bandwidth
(Hz); and
KIdc B
Iflicker noise =
,
(4)
f
where Idc is the average value of direct current (A), f is the
frequency (Hz) and K is a constant that depends on the type of
material and its geometry.
The results were used to calculate the performance
limitation of accelerometers, sensing probe cantilevers and
thermal infrared detectors. Figure 2 shows the model of
a capacitive accelerometer and the associated circuit. It
is a schematic diagram of a MEMS accelerometer with a
differential capacitance means of detecting the relative motion
of the proof mass due to inertia. The device illustrated uses
force feedback to maintain the position of the mass near its
position for zero acceleration.
In another work, Djuric et al (2002) derived the equivalent
noise model for a microcantilever.
The study found
adsorption–desorption processes, temperature fluctuations
and Johnson noise as the dominant noise sources in
microcantilevers at high frequencies, whereas the adsorption–
desorption noise dominated at low frequencies.
Another similar study extracted noise parameters for the
macro-modeling of MEMS (Greiner and Korvink 1998). The
work investigated the noise sources in the mechanical energy
domain, where the noise was described by a correlation
function under different operating conditions. The correlation
functions of the different dissipation channels were developed
using a vibrating micro bar as a practical example.
One theoretical study of noise in MEMS-based resonators
was done by Vig and Kim (1999). The work discussed
the stability of resonators as the dimensions of the devices
6. Measurement techniques
In general, a noise measurement system consists of device
under test (DUT), low-noise amplifier, spectrum analyzer and
computer for data plotting and analysis. Figure 3 shows
the typical noise measurement for MEMS inertial sensors.
The noise voltage output from the DUT is fed to the low-noise
amplifier (LNA), which is used as a front-end amplifier. The
LNA amplifies the noise voltage without adding significant
noise, and then the amplified noise voltage is fed into the
spectral analyzer. The analyzer measures the power spectrum
of the noise signal and displays the results on logarithmic scale
such as dBm. In most modern measurements, data from the
analyzers are fed to the personal computer via a GPIB cable
for analysis.
Figure 4 shows a method used to measure SAW resonator
phase noise (Enguang 2002). In this setup, a phase bridge
is used to differentiate the phase of two signals, namely the
referenced signal and the measured signal coming from the
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Meas. Sci. Technol. 21 (2010) 012001
Topical Review
Figure 3. Typical setup of a low-frequency noise measurement system (Mohd-Yasin et al 2009).
Figure 4. Setup to measure phase noise from surface acoustic wave devices (Enguang 2002). The HP 11484A is the phase bridge referred
to in the text.
further processing. An FFT was performed to obtain the noise
spectra from 0.5 to 30 kHz.
SAW resonator (DUT). The HP8663 A synthesizer provides
the low-noise carrier signal which is split into two signals. The
first half acts as a referenced signal that goes to the one arm of
the phase bridge. The second half of the signal is injected into
the input of the two-port SAW resonator DUTs. The DUT is
mounted in a chamber filled with sample gas that would cause
frequency shifts at the output of the resonator. The output
signal is then fed to another arm of the phase bridge. The
lengths of the DUT and non-DUT signal paths connected to
the phase bridge are adjusted to obtain the phase quadrature at
the phase detector, which is then fed to HP11848 A phase noise
interface unit. The data are copied by the HP2763 A plotter,
and the phase noise is displayed on the HP3585 A spectrum
analyzer or the HP3561 dynamic signal analyzer.
An example of the setup to measure the noise amplitude of
a chemical sensor is shown in figure 5 (Hoel et al 2002). In this
work, an Au thin film was coated with tungsten trioxide, which
produces conductance noise at the output of the sensor. A fourpoint measurement setup with a dc current generator was used
to detect the signal fluctuations, shown in part (a). The voltage
fluctuations represent the resistance, which is the conduction
noise of the sensor. The amplitude of the fluctuation is
proportional to the amplitude of the noise. The measurement
was ac coupled to the input of the FET differential amplifier,
which amplified the signal to 80 dB, and converted it to digital
data with an NI 16 bit ADC. The data were fed to the PC for
7. Common MEMS structures
The field of MEMS involves some characteristic and broadly
applicable microstructures, which can be used in a variety
of applications. Examples are cantilevers and other types
of resonant micro-mechanical structures. Structures with
varying capacitance, due to the motion of facing plates or
inter-digitated parts, are common in many devices. The few,
quite recent studies of noise in these widely useful structures
are surveyed in this section.
Microcantilevers are especially useful in diverse MEMS
sensors, most notably as the active element in atomic
force microscopes (AFM) for imaging surfaces with atomic
resolution and for manipulating molecules on surfaces. They
have also been shown to be useful for measuring accelerations,
as the active element in radio-frequency switches, as part of
micro-fluidic systems and for mass and bio-chemical sensing.
Both commercial cantilevers and research structures have
been employed in MEMS noise studies. McLoughlin et al
(2007) measured the power spectral distribution of AFM
cantilevers immersed in solutions of poly(ethylene glycol)
over temperatures of 23–33 ◦ C. Optical reflectivity means
of measuring displacements were employed with a spectrum
analyzer to record noise spectra. The data were used to
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Meas. Sci. Technol. 21 (2010) 012001
Topical Review
(a)
(b)
Figure 5. (a) A schematic perspective view of a noise sensor device. (b) Electronic setup to measure the noise (Hoel et al 2002).
obtain the numerical values of the density and viscosity of the
fluids, which compared well with values from the literature
that were measured using macroscopic instruments. The work
opens the possibility of measuring fluid properties with very
small samples, possibly in micro-fluidic systems. Specially
fabricated doped silicon microcantilevers were used by Lee
et al (2008) to obtain resonance behavior and noise spectra
in the range of 25–175 ◦ C. Both local and uniform heating
were employed. For the geometries used, local heating had
a greater effect on changes in the resonance frequency of
the cantilevers. The key point from such studies and other
applications of microcantilevers is the fact that thermally
induced, noisy motions can be exploited for applications or
used to modify the mechanical behavior of the structures.
Resonant MEMS structures, besides cantilevers, are also
widely useful. They can range from simple beams clamped
on both ends to complex structures with inter-digitated fingers
that are suspended on springs. Depending on the size and
ambient atmosphere, such structures are subject to thermomechanical noise, including Brownian motion and absorption–
desorption noise. In one recent study, Sharma et al (2008) did
an analysis and optimization for noise in MEMS resonant
structures. They compared finite element calculations with
parametric expressions for squeezed-film damping obtained
from analytical models. This permitted extraction of a
behavioral model for the resonant vibratory ‘gyroscope’, that
is, an angular rate senor based on the Coriolis force. Both
thermo-mechanical and electronic noises were taken into
account. There is great room for additional studies of noise in
resonant structures.
The following sections deal with the various types of
noise measured in the different classes of MEMS, which have
various applications. The specific microstructures and noise
measurement techniques used to obtain the results, which are
reviewed, can be found in the references.
performance of systems, especially when operating under low
acceleration conditions.
Three groups in Japan, the USA and Holland have
modeled and characterized noise of custom-made capacitive
micro-accelerometers. The Japanese group used a linear
noise model to simulate and measure the thermal–mechanical
and input-referred noise characteristics for a capacitive-servo
accelerometer (Yoshida et al 2005). University of Michigan
researchers constitute one of the leading groups in designing
ultrasensitive micro-accelerometers that are able to detect
micro-g (gravity) levels (Kulah et al 2006). They discovered
that the mechanical noise is generally dominant, and therefore
designed the sensor structure with large proof mass and
small damping factor. The third work by the Dutch group
attempted to characterize directly the mechanical–thermal
noise spectrum by repeatedly bringing the capacitive microsensor to pull-in, and measuring the pull-in time, followed by
an FFT (Rocha et al 2005). They found that the white noise
level is in agreement with existing theory on damping, and that
the 1/f noise is independent of the ambient gas pressure.
Oropeza-Ramos et al (2008) performed the noise analysis
of a tunneling accelerometer. The custom device had
been fabricated with a low-noise differential transresistance
amplifier with a large gain. The dynamic model of the closed
loop system was constructed using stochastic control theory.
Thermo-mechanical noise from the proof mass motion, shot
noise from the tunneling junction and Johnson resistor noise
were considered. The analysis was based on a linearized
model, similar to the approach of Yoshida et al (2005).
They found a 30% difference between the theoretical and
experimental standard deviations of the tunneling signal,
which was attributed to the inaccuracies of the work function
() in the tunneling model.
The author’s group performed a study of noise in
commercial MEMS accelerometers (Mohd-Yasin et al 2003,
2007, 2008). The noise spectrum was measured as a function
of the acceleration of gravity in the range from −1 to
+1 g. A common spectral behavior of noise was found,
with approximately 1/f noise dominating at low frequencies
and white thermal noise being the limiting factor at higher
frequencies. Unexpected resonances were also observed
in three commercial devices. Figure 6 shows the noise
characteristics for ADXL105 from Analog Devices. They
were measured with the setup shown in figure 3.
8. Accelerometers
MEMS accelerometers are the most mature product among
inertial MEMS. Major markets for MEMS accelerometers
are automobile airbag triggers, earthquake detection circuits,
health care, toys, cameras and cell phones.
Since
MEMS accelerometers are used in many systems, the noise
characteristics of these devices are important. They limit the
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Meas. Sci. Technol. 21 (2010) 012001
Topical Review
Figure 6. ADXL105 noise characteristics at zero gravity (Mohd-Yasin et al 2008). The peaks are due to the harmonics of the oscillator
inside the chip, and are not noise.
(This figure is in colour only in the electronic version)
Figure 7. Performance of micro-accelerometers in terms of noise floor versus year (Chae et al 2004).
Apart from noise measurements of MEMS
accelerometers, several designers have used noise theory
to increase the sensitivity of their sensors. The most prominent
group is led by Professor Najafi from University of Michigan.
In Yazdi and Najafi (2000), the modeling and noise analyses
of closed-loop micro-g accelerometers with deposited rigid
electrodes were performed. This work identified several types
of noise sources that affect micro-accelerometers, such as
mechanical noise, thermal noise, amplifier noise, sensorcharging reference voltage noise, clock jitter noise and
quantization noise. Chae et al (2004) produced a nice
summary of the progress in developing low-noise microaccelerometers, as shown in figure 7.
Noise modeling and analysis were also performed with
tunneling accelerometers (Liu and Kenny 2001, Yeh and
Najafi 1997a), automotive accelerometers (Joseph et al 1996)
and resonant micro-accelerometers (Seshia et al 2002). All
these studies focused on accelerometer’s noise characteristics
under static conditions. However, two works were able to
study noise characteristics under dynamic conditions. In Han
and Cho (2003), the performance of an accelerometer and
its noise characteristics were recorded with varying voltages
and pressures. In Liu et al (1998), a shake table was used
to create dynamic accelerations to measure noise and other
characteristics of a tunneling accelerometer. In addition to the
noise research mentioned above, there are many works that
used noise theories to optimize accelerometer designs (Boser
and Howe 1996, Yazdi et al 2003, Yeh and Najafi 1997a, Kajita
et al 2002, Monajemi and Ayazi 2006, Amini and Ayazi 2005).
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Meas. Sci. Technol. 21 (2010) 012001
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oscillator readout on the same chip in an effort to reduce noise
(Oysted and Wisland 2005). A theoretical and computational
study of noise in MEMS pressure sensors compared the
performance of three readout mechanisms (Pattnaik et al
2005). It was found that the noise-equivalent pressure for a
guided wave optical pressure sensor was much smaller than for
either capacitive or piezoresistive readouts. Clearly, there are
many opportunities for experimental noise studies in MEMS
pressure sensors with diverse readout mechanisms.
9. Angular rate sensors
MEMS ‘gyroscopes’, more accurately known as angular rate
sensors, have increasingly taken the place of conventional
rate sensors in many applications. There are three primary
works that investigated the noise properties of a MEMS
gyroscope. The first studied the effect of mechanical–thermal
fluctuations on a vibrating-mass surface-micromachined
gyroscope (Annovazi-Lodi and Merlo 1999). It was found that
the mechanical–thermal noise source represents a practical
sensitivity limit in the gyroscope and is likely to restrict
their performance, even in automotive applications that do
not require high sensitivity. The study concluded that the
vibrating-mass surface-micromachined gyroscope structure
would require a significant dimension increase or a completely
different design to lower the noise floor and increase the
sensitivity. The second work extended the first by considering
the effect of the angular random walk, the noise-equivalent
rotation rate and the spectral density of the noise component
of the rate measurement (Leland 2005). The third paper
(Lin and Stern 2002) analyzed the behavior of a DSP-based
correlation filter used to mitigate the effects of thermal noise
in a low-cost MEMS gyroscope. It discusses the mechanical
thermal noise and its simulated effect on the performance of the
gyroscope.
Many gyroscopes designers take into consideration noise
factors to improve the performance of their designs. The
earliest work is by Degani et al (1998). It derived the
noise-equivalent rate (NER) of a rate gyroscope, among
others, including the mechanical behavior, optical sensing and
electronics in order to derive an optimal design approach.
Designers have also utilized different types of sensing
mechanisms such as tuning forks, oscillating wheels, Foucault
pendulums and ‘wine glass’ resonators to obtain angular rates.
In all cases, noise is one of the main factors that has been
taken into the design consideration. Three works (Seshia et al
2002, Xie and Fedder 2003, Shcheglov et al 2000) discussed
the effects of electrical–thermal noise in a resonant-output
gyroscope, a deep-reactive-ion-etch (DRIE) CMOS gyroscope
and a Jet Propulsion Lab (JPL) gyroscope. The last work on
the JPL gyroscope concentrated on the effect of noise at high
temperature because of its intended applications in aerospace.
The latest work from University of Berkeley attempted to
reduce the effect of electrical noise from the interface circuitry
of inertial sensors (Petkov and Boser 2005). In addition
to all the studies mentioned above, there is one practical
study (Palaniappan et al 2003), which compared several key
parameters such as noise floor of two different integrated
surface micromachined z-axis frame-gyroscopes that were
fabricated on the same chip.
11. Microphones
Microphones are devices to measure high-frequency pressure
variations, that is, audible and ultrasound signals. There
are several studies of noise in microphones. In many
MEMS acoustic sensors, the amplitude of input-referred (or
electronics) noise of the attached preamplifier stage is much
larger than the noise from within the sensors. In such cases, the
electronics noise is the dominant source with a high acoustical
equivalent input noise. In other devices, thermo-mechanical
noise from inside a microphone dominates.
Numerous studies were performed to investigate the noise
properties, and most importantly, to optimize the SNR in
acoustic sensors. Several research papers are reviewed next.
The earliest was performed by Gabrielson (1995), when he
studied the fundamental noise limits for miniature acoustic
and vibration sensors. The paper reviewed several techniques
for evaluating noise in acoustic and vibration sensors, in
general, and in micromachine sensors, in particular, taking into
considerations three factors. The first is the addition of a whitenoise force generator for each component of the mechanical
resistance. The second is the distribution of the equipartition
noise power according to the frequency response of the sensor.
And, the third is the application of a software electroniccircuit simulator to the mechanical equivalent circuit of a
device. Gabrielson’s work also discussed the complementary
relationship of shot noise (nonequilibrium) and thermal noise
(equilibrium).
The second study was performed at NASA Langley. The
researchers measured noise from air condenser, piezoresistive,
electret condenser and ceramic microphones (Zuckerwar et al
2003). Theoretical models of the respective noise sources
within each microphone were developed, and then used
to derive analytical expressions for the total noise power
spectral densities. Several additional noise sources for
the piezoresistive and electret microphones were modeled,
and found to contribute significantly to the total noise.
Experimental background noise measurements were taken
using an upgraded acoustic isolation vessel and the data
acquisition system. Those results were compared to the
derived models. The models were found to yield power
spectral densities consistent with the experimental results.
The findings showed that the 1/f noise coefficient is
strongly correlated with the diaphragm damping resistance,
irrespective of the detection technology, i.e. air condenser or
piezoresistive.
In the third research project, researchers from Knowles
Electronics made noise measurements on their MEMS
10. Pressure sensors
Along with accelerometers, pressure sensors are a main
commercial success of MEMS. They generally measure lowbandwidth pressure variations. Interestingly, there are few
studies of noise in low-frequency pressure sensors. One
project integrated a piezoresistive pressure sensor with ring
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miniature electret microphone, typically used in hearing aids
(Thompson et al 2002). A circuit model was developed
from the measured data to determine the noise sources within
the microphone. The dominant noise source depends on
the frequency range. Electrical noise from the amplifier
circuit that buffers the electrical signal from the microphone
diaphragm is dominant above 9–40 Hz. Thermal noise
originating in the acoustic flow resistance of the small
hole present in the diaphragm to equalize barometric pressure
dominates after that up to 1 kHz. Between 1 kHz and
9 kHz, the primary noise originates from the acoustic flow
resistances of sound entering the microphone and propagating
to the diaphragm.
The fourth study was on the characterization and noise
analysis of capacitive MEMS acoustic emission transducers.
Acoustic emission as an ultrasonic wave is generated when
elastic energy is released in a structure by permanent and
irreversible change. It is widely used to detect and locate faults
in the structure. Resonant-type capacitive MEMS transducers
were developed at Carnegie Mellon University for the above
purpose. Wu et al (2007) reported the noise analysis and gave
a discussion of noise sources of the devices. Their analysis
identified Brownian noise, caused by collisions between the air
molecules and suspended diaphragm, as the dominant source.
Furthermore, they observed that the noise is independent of
the quality factor (Q) of the transducer.
Research conducted at the University of Florida
investigated the excess noise in a silicon piezoresisitve
microphone (Dieme et al 2006). This group measured
the noise power spectra for both commercial and researchprototype MEMS piezoresistive microphones as a function of
applied voltage bias for both free and blocked membranes.
They found evidence that the fundamental noise sources
are divided into frequency-independent thermal noise and
frequency-dependent 1/f excess noise, where the latter
dominates at low frequencies. They also found a bias
dependence and membrane independence of the output noise,
indicating that the primary source of the excess noise is
electrical in origin.
Another work characterized a piezoresistive silicon
microphone designed for aeroacoustic measurements (Arnold
et al 2001). These devices were characterized in terms
of linearity, frequency response, drift, noise and power.
Measurements of the noise power spectral densities for eight
microphones, biased at 3 V, were performed in a Faraday cage.
Figure 8 shows a plot of the noise measured with a DUT versus
the system noise. The 1/f noise intersects with the thermal
noise at approximately 10 kHz for the DUT. The hump in the
data between 1 and 10 kHz is believed to be the result of a
trap mechanism. The spikes in the data are from deterministic
interference at harmonics of 60 Hz and 20 kHz. Since the
signals are present in both measurements, their effect can be
negated by subtraction of total power at each frequency.
Beside these five noise studies, many MEMS microphone
designers investigated the noise sources of their products. The
design and fabrication of a low-voltage, low-noise differential
silicon microphone was described (Rombach 2002). The
microphone was designed with two back-plates for two
Figure 8. Noise PSD of a piezoresistive silicon microphone (Arnold
et al 2001).
advantages.
Firstly, the microphone could offer twice
the signal of a single back-plate microphone due to the
symmetrical arrangement of the two back-plates. Secondly,
the bias field was 30% higher compared to a single back-plate
microphone, resulting in higher sensitivity and wider linear
dynamic range. The noise performance was measured using
a low-noise amplifier and an FFT analyzer. It was observed
that at lower frequencies, the spectrum was dominated by
the ambient acoustical noise up to a few kHz. Further
investigation would be required to find the source of the white
noise that caused the offset in the noise spectrum. This
work indicated that the white noise might have originated
from a higher serial resistance of the silicon back-plates and
membrane.
Another study developed a general SPICE-based model
of a silicon microphone system (Brauer et al 2004). The
acoustical and mechanical, as well as electrical behaviors of the
microphone were considered in developing the SPICE model.
The model also took into consideration the effect of individual
noise sources and their contributions to the total noise. Several
experiments were performed to obtain the key parameters to
develop the model. The measurements for sensitivity and
noise characteristics were performed in a pressure chamber.
In that experiment, the dimensions of the chamber were small
enough to prevent the reflections of acoustic waves; hence, the
pressure was constant at any position. The noise was measured
in the same chamber, but with a greater accuracy because of
grounding to prevent electromagnetic influence.
Further analysis indicated the effects of individual noise
sources on the silicon microphone. Figure 9 shows the
amplitude of the noise sources as a function of frequency.
It was observed that two noise sources dominate, namely the
load resistance, Rload , which injects electrical charges into the
membrane, and the acoustical resistance, Rhole , which is the
resistance through the perforated back-plate.
In addition to the above noise studies on silicon
microphones, several designers (Ko et al 2002, Neumann
and Gabriel 2001, Scheeper et al 2003) use noise theories
to enhance the sensitivities of their devices.
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Meas. Sci. Technol. 21 (2010) 012001
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Figure 9. Plot of the contribution of individual noise sources for a
silicon microphone (Brauer et al 2004).
Figure 10. Physical model of optical cavity with thermal noise
force (FN ) included (Tucker et al 2002).
12. Optical MEMS
Another study (Supino and Talghader 2002) analyzed the
thermal properties of a tip-tilt micromirror for the operation
in air and vacuum. The studies of noise sources associated
with tip-tilt micromirrors were performed analytically and
experimentally.
This work concluded that three noise
mechanisms were present in micromirrors, namely Johnson
noise, 1/f noise and thermal conductance noise. The first
two were standard noise mechanisms that were present in
all resistor-type devices. Thermal conductance noise became
significant if the device had a small thermal mass.
Two projects at University of Berkeley (Zhao et al
2002, Choi et al 2004) designed, fabricated and tested an
optomechanical uncooled infrared imaging system. Detailed
noise analysis was performed to find the noise-equivalent
temperature difference (NETD) of this system, which was
determined from the system’s total noise level. All noise
sources were analyzed to compute the total noise. The first
source was thermodynamic fluctuation noise. This noise
source exists in a thermodynamic system that exhibits random
fluctuations in temperature, based on the statistical nature of
the heat exchange with the environment. The second was
temperature fluctuations caused by temperature instabilities
on the substrate. The third noise source was vibration noise
that originated from thermal and external sources. The last
noise source was the optical readout noise, both from CCD
and the laser. Figure 11 shows the total noise spectrum of the
light intensity from the vertical cavity surface laser operating
at 800 nm.
In addition to these papers, several works covered the
effects of noise on the performance of optical systems. The
effect of quantum noise on an optical sensor for a gyroscope
system was presented (Armenise et al 2001). One group
analyzed the noise factor in an optical passive ring resonator
gyro (Suzuki et al 2000). Another paper discussed noise
effects on a Hadamard-transform spectrometer (Diehl et al
1999). In the latest design of tunable vertical cavity surface
emitting lasers (VCSELs), the MEMS mirror used wavelength
feedback systems to reduce the Brownian motion that broadens
the spectral width of the laser emission (Huber et al 2004).
Thermal noise is the dominant noise source in optical MEMS.
This is due to the fact that thermal energy induces motion
in opto-mechanical devices. This type of noise limits the
spectral resolution in optical cavities or the sensitivity of the
cantilever mass detectors with optical readouts (as discussed
in section 7). One paper surveyed some of the most common
thermal effects in micro-mechanical optics (Talghader 2004).
It reviewed the fundamental heat transfer mechanisms of
conduction, convection and radiation, in regard to typical
micromirror structures. A simple measurement technique to
extract thermal conductance was described. The interface
thermal conductance was discussed using recent experimental
data on actuated micro-mechanical structures and squeezedfilm theory. The paper also explained deformation due to
thermal expansion in terms of an analytical elastic model.
Another work by Tucker et al (2002) examined the thermal
noise and radiation pressure effects in MEMS Fabry–Perot
tunable filters and lasers. Both applications require cavities
with extremely high mechanical stability. Small perturbations
in mirror motion caused by thermal noise degrade the spectral
resolution. The Fabry–Perot optical cavity model is shown in
figure 10.
The cavity consisted of a fixed mirror and a movable
mirror. In the movable mirror, the fluctuations in mechanical
energy along the optical axis were set equal to the average
thermal energy in each degree of freedom. The mean squared
deviation in the position of the mirror x2 is indicated in
figure 10. The model showed that the change in mirror position
caused a change in the cavity length, and therefore a change in
the cavity resonance. The work also examined the frequency
response of the thermal-mechanical noise. The mirror position
was expected to fluctuate on the time scale of the order of, or
longer than, the mechanical response time. But the amplitude
of fluctuations should fall off rapidly at frequencies higher
than the inverse of that time. A small signal analysis using
a force equation for mirror position and voltage showed that
the frequency response of the resonance was that of a standard
second-order low-pass filter.
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Meas. Sci. Technol. 21 (2010) 012001
Topical Review
and metal-to-metal contact series MEMS switches. Several
interesting observations about phase noise were made. First,
a well-designed MEMS shunt switch possesses a negligible
phase noise from thermal mechanical effects (Brownian noise).
The phase noise was found to be so low that it was hard
to measure using even the best phase noise measurement
equipment. However, it was also observed that low-resistance
shunt switches, and switches that were suspended at low gap
heights, gave 20–40 dB higher phase noise. Second, varactorbased phase shifters had a relatively high phase noise due
to the capacitances used in the design. Third, distributed
phase shifters had phase noise that was around 20 dB lower
than the varactor-based design, but still 20 dB higher than
switched network designs. Fourth, the series switches had
virtually no phase noise in the reflect mode, since their up-state
capacitance was extremely low. This work also concluded that
the contributions of acceleration, acoustic and bias voltage
noise on MEMS phase shifters and switches were quite low
for an acceleration noise of 10 g or less, an acoustic sound
pressure level (SPL) of 74 dB or less and a voltage bias
noise of 0.3 V or less. A similar approach in the subsequent
work was used to analyze noise of RF MEMS switches,
varactors and tunable filters (Dussopt and Rebeiz 2004). The
latest work by Kaajakari et al (2005) analyzed phase noise
in capacitively coupled microresonator-based oscillators. A
detailed analysis of noise mixing mechanisms in the resonator
was presented. Capacitive transduction was shown to be the
dominant mechanism for low-frequency 1/f -noise mixing
into the carrier sidebands.
In another work, static phase noise and vibration
sensitivity of a thin-film resonator (TFR) filter operated at
640 and 2110 MHz were measured (Birdsall et al 2002). The
evaluation of the TFR filter’s short-term frequency stability and
vibration sensitivity was accomplished by installing the filter
under test as the frequency control element in an oscillator
with a low loop delay. A 50 amplifier was used in the setup
as the oscillator sustaining stage. The results of the experiment
showed that the short-term frequency instabilities of the TFR
filters were small compared to those induced in the oscillator
signal by the sustaining 50 amplifier phase modulated (PM)
noise.
A fourth study involved accurate simulation of phase noise
in MEMS voltage control oscillator (VCO) circuits (Behera
et al 2005). This work employed the numerical solution of
device level equations to compute the capacitance of a MEMS
capacitor. The phase noise was then determined by combining
the computed noise from the MEMS capacitor with a nonlinear
circuit-level noise analysis. To ensure an accurate simulation,
this capacitor model took into consideration the effects of
three noise sources: oscillator phase noise, which consisted of
electrical thermal noise, 1/f noise and mechanical–thermal
vibration noise. After the completion of the capacitor model,
the circuitry for the MEMS VCO was used to perform the
nonlinear noise analysis. An 800 MHz single-ended Colpitts
VCO implemented in HP 0.8 μm CMOS technology was
chosen for this purpose. Figure 12 shows the simulated noise
spectrum of the modified MEMS VCO. The offset frequency
is referenced to the mechanical resonant frequency. The
Figure 11. Noise spectrum of the light intensity from a vertical
cavity surface laser with a wavelength of 800 mm. The relative
noise (I/I) over 30 Hz BW is dominated by low-frequency noise
(Zhao et al 2002).
13. RF MEMS
RF MEMS cover a large range of devices from simple
inductors and filters to complex systems such as voltagecontrol oscillators (VCO). MEMS RF switches are available
commercially. Many studies of the noise characteristics of
RF MEMS are available. In general, the phase noise is the
dominant noise source for RF MEMS. This section highlights
noise research on MEMS RF devices, including an inductor,
switches and a switch-based phase shifter, resonator, voltage
control oscillator and resonator oscillator.
The first paper reported the noise associated with
mechanical deformation of a MEMS inductor (Dahlmann
and Yeatman 2002). The device was fabricated in a fully
parallel surface micromachining process. One concern about
this fabrication approach was that the suspended inductor
or the membrane supporting the inductor was susceptible
to mechanical loading. Therefore, this study attempted to
estimate the variation of the electrical characteristics and the
associated noise that was due to the physical deformation of
the structure. The geometric model was developed based on
the fabricated inductor. The estimation of the noise due to
mechanical deformation was carried out in three steps. First,
the deformation was calculated numerically as a function of
the mechanical loading. Second, the change in inductance
was calculated numerically as a function of displacement.
Computer programs were used to perform the calculations
in both steps. Finally, the noise power due to amplitude and
phase variation of the RF signal was calculated analytically.
From the data obtained, it was concluded that the amplitude of
the signal noise could be equal to or greater than the thermal
noise depending on three factors, namely the bandwidth of the
system, the signal amplitude and the mechanical loading.
A second paper analyzed the effects of Brownian noise,
acceleration, acoustic and power supply noise on a switchbased phase shifter (delay) circuit (Rebeiz 2002b). The
analysis was performed for capacitive-shunt MEMS switches
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Meas. Sci. Technol. 21 (2010) 012001
Topical Review
Figure 13. Measurement results for a MEMS resonator (Lee and
Nguyen 2003). The acronyms are defined in the text.
second circuit controlled the sustaining amplifier gain, called
Av -ALC. The results of the measurement with and without
ALC engaged are given in figure 13. The results showed
that the MEMS resonator oscillator exhibited 1/f 3 phase
noise without the Vp-ALC and both 1/f 3 and 1/f 5 phase
noise components when Vp-ALC was engaged. The work
further investigated the origin of the noise components. It was
found that the noise components originated primarily from
the nonlinearity in the voltage-to-force capacitive transducer,
either through direct aliasing of amplifier 1/f noise or through
instabilities introduced by spring softening phenomena. The
group investigated the noise characteristics of other resonator
designs (Nguyen and Howe 1994, 1999, Jing et al 2004).
Noise studies of resonators seemed to attract the interest of
many groups. One of the studies was performed in Columbia
University (Dec and Suyama 2000) and another by Stanford
researchers (Agarwal et al 2006). It is worth noting that the
latest studies of noise in resonators involve nano-scale devices
(Vig and Kim 1999, Tamayo 2005, Cleland and Rourkes 2002).
Figure 12. Simulated noise spectrum of a MEMS voltage controlled
oscillator (Behera et al 2005).
Table 2. Values of the phase noise at three different frequencies
(Behera et al 2005).
Offset
frequency
Measured
(Qm = 15)
Simulated
(Qm = 15)
Simulated
(Qm = 5)
Simulated
(Qm = 1)
10 kHz
100 kHz
3 MHz
−81
−110
−139
−80.4
−109.1
−140.8
−77.6
−109.1
−140.8
−73.1
−108.9
140.8
contributions of individual noise sources are shown in the
figure. It was observed that, at low offset frequency, the
1/f noise dominated and, the phase noise showed a 30 dB
per decade fall. The electrical-thermal noise dominated for
frequencies five times and more above the mechanical resonant
frequency of 20 kHz, where the phase noise showed a 20 dB
per decade decay.
The simulated values of the total phase noise for different
values of quality factors, Qm , were calculated in the second
part of the work. The results showed that an improvement
in phase noise could be seen for increasing Qm at low offset
frequencies. However, as the offset frequency became greater,
the dependence of the phase noise on Qm was reduced. Table 2
shows the values of the phase noise for different Qm at three
different offset frequencies, 10 kHz, 100 kHz and 3 MHz.
Similar work to simulate and model the noise of MEMS
varactor-based RF VCOs was performed by Sankaranarayanan
and Mayaram (2007). The mechanical noise exhibited by the
MEMS varactor was presented. It originates from Brownian
motion. The Brownian motion transforms to a noise current.
A noise current model was therefore used to describe the upconversion mechanism, which was translated to phase noise.
Another work showed the influence of an automatic level
control (ALC) circuit on an oscillator phase noise of a MEMS
resonator (Lee and Nguyen 2003). The 10 MHz MEMSbased resonator oscillator was used as the device under test.
This custom-designed system allowed the series oscillator
to be controlled by two external ALC circuits. The first
circuit controlled the resonator’s dc bias, called Vp-ALC. The
14. SAW devices
Notable work on noise of a SAW device was performed by
Enguang (2002). He conducted theoretical and experimental
studies of surface-related phase noise of SAW resonators.
The surface phase noise was viewed as a stochastic process
resulting from particle molecular adsorption and desorption
processes on the device surface. SAW devices have the specific
property of extremely high surface sensitivity. They are very
prone to be perturbed by mass loading of gas molecules,
which this work predicted was the possible source of the noise
characteristics. Based on the data, it was found that some
volatile vapors, which interacted with the SAW resonator,
were able to change the resonator’s noise characteristics.
These changes were generated by variations in the rate of
adsorption and desorption of the surface particles. This work
also predicted that the surface molecular motion noise might
exist in other electronic devices as the dimensions shrink.
The next two works employed SAW devices as chemical
sensors. McGill et al (1998) compared the performance
of SAW chemical sensors that used a variety of coating
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Meas. Sci. Technol. 21 (2010) 012001
Topical Review
Table 3. Calculated oscillator phase noise performance and spectral densities of frequency fluctuations using measured residual phase noise
data from SAW devices with various deposition techniques (McGill et al 1998).
Device
Flicker
coefficient (rad Hz−1 )2
Deposition
technique
Residual noise
floor (dBc Hz−1 )
Loaded Q
Losc (1) (dBc Hz−1 )
Sδf (1) (Hz2 Hz−1 )
1
2
3
4
5
6
7
4.0 × 10−38
5.14 × 10−38
1.2 × 10−34
5.3 × 10−37
2.3 × 10−36
7.22 × 10−37
1.6 × 10−36
Uncoated
Uncoated
Aerosol
Aerosol
MAPLE
MAPLE
MAPLEb
−160
−160
−160
−160
−160a
−160a
−160a
7922
7012
3244
5486
6747
7440
5643
−38
−37
−4.0
−27.5
−21.5
−26
−21
0.16 × 10−3
0.2 × 10−3
0.4
1.78 × 10−3
7 × 10−3
2.5 × 10−3
8 × 10−3
a
b
Estimated value.
MuIitple resonance modes observed, amplifier flicker noise coeff = 5.02 × 10−14 .
materials and deposition techniques. Residual phase noise
measurements were made as one of the performance
parameters. The noise measurements were performed on SAW
sensors with and without polymer coatings. The residual phase
noise at 1 Hz, the white noise floor, the power law dependence
on the offset frequency and the 1/f corner were measured.
This work predicted the system performance of SAW sensors
based on measured data and the modified Leeson’s noise model
of the loop oscillator, as shown in table 3.
They concluded that the polymer spray-coated SAW
devices exhibited large variation of the loaded quality factor
(Q) and residual phase noise. In some cases, additional 1/f 2
noise dependences existed when the frequency of the phase
noise exceeded the bandwidth of the resonator. Furthermore,
there was no obvious correlation between loaded Q and the
phase noise.
Figure 14. Flow sensor output voltage and noise from the amplifier
and flow sensor (Radhakrishnan and Lal 2003)
make the device more immune to flow-induced temperature
changes.
We also found another study that injected white noise
into the circuits of the micro-fluidic flow sensor (Law and
Afromowitz 2000). This was deliberately done to characterize
the performance of the sensor with and without the white noise
source. Besides these works, there are a few reports of noise
analyses to determine the limit of sensitivity of particular flow
sensor designs (Yoon and Wise 1992, Wu et al 2000, Kaltsas
and Nassiopoulou 1999).
15. Flow sensors
Flow sensors are one of the emerging MEMS products.
Because they are still in development stage, few works were
found on the noise studies for flow sensors. In one project
(Radhakrishnan and Lal 2002, 2003), the Cornell researchers
presented a scalable microchannel-embedded cantilever flow
sensor with electronic readout. The scalable nature of the
sensor addressed the need to employ arrays of flow sensors to
characterize localized flow patterns. The electronic readout
addressed the need to integrate flow sensors in micro-fluidic
channels for closed-loop flow control. The group also
presented a prediction of the noise characteristics for flow
measurements, based on the results obtained using prototype
flow sensors. It was observed that electrical-thermal noise was
the main noise source. This thermal noise originated from the
resistors used in a Wheatstone bridge in the interface circuitry
of the flow sensor. Figure 14 presents the results of the noise
analysis. The data showed that the noise came from two
sources: the amplifier and the flow sensor. The experimental
results also showed that the flow in the channel caused thermal
gradients along the channel, which affected the performance
of the device considerably. This work suggested the use of
nickel cantilever beams to shunt away any thermal fluctuations
that existed in the channel.
This improvement would
16. Chemical sensors
Miniaturization is the recent trend in analytical chemistry
and life sciences. The applications cover a broad range,
including micro arrays, DNA sequencing, sample preparation
devices, and cell separation and detection functions, as well
as environment monitoring with gas sensors (Nguyen and Wu
2005). The number of archival journal papers in this area has
increased drastically over the past few years. We first review
several papers on noise in chemical sensors. The next section
will be on noise in bio-MEMS.
One of the notable studies was performed Hoel et al
(2002), where the conduction noise measurements were
carried out within 0.3–45 Hz frequency range for Au
films covered by a thin layer of tungsten trioxide (WO3 )
nanoparticles. An ‘invasion noise model’ was developed based
on the data collected from the experiment. This model was
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Meas. Sci. Technol. 21 (2010) 012001
Topical Review
founded on the idea that the noise was related to the insertion
and extraction of mobile chemical species, in this case onto and
from the WO3 nanoparticles. The results show that exposing
the Au and WO3 films to alcohol vapor will gradually increase
the noise intensity, which went to a maximum after 15 min.
Another study used the noise characteristics to improve
the selectivity of semiconductor sensors (Shaposhnik et al
2005). The total noise PSD of the sensors were composed
of both chemisorption of gases and vapors, and chemical
reactions between reducing gases and air oxygen that occur on
the sensor surface. A gas sensor designed for odor recognition
of a complex sample could be realized by combining the
electric resistance and its noise characteristics. Similar work
was performed by Kish et al (2000), whereby electronic noses
and tongues utilized the conduction noise data, taken at the
output of a chemical sensor. It is shown that a single sensor
may be sufficient for realizing an electronic nose or tongue for
several analytes.
Several groups developed noise models of chemical
sensors. Gomri et al (2005, 2006) proposed a theoretical
description of adsorption–desorption noise in metal oxide gas
sensors using Langmuir and Wolkentein models. They found
that the adsorption–desorption noise (A–D noise) part of the
total noise spectra has a Lorentzian distribution, and applied
the proposed model for simulating the oxygen chemisorptioninduced noise of the metallic-oxide gas sensors. Another
work from the Stanford researchers proposed a general circuit
model for the electrical noise of electrode–electrolyte systems,
intended for electrochemical sensors (Hassibi et al 2004). In
their approach, the analytical model of all the noise sources
that contributed to the overall noise PSD of the system
was calculated. They showed that the current and voltage
fluctuations originated from either thermal equilibrium noise
created by conductors, or nonequilibrium excess noise caused
by charge transfer processes produced by electrochemical
interactions. The presented electrical noise model could be
used to explain thermal noise in sensing electrodes, shot
noise in electrochemical batteries and 1/f noise in corrosive
interfaces. In addition to these works, there are several
chemical sensor designers who performed noise analysis on
their devices, such as in Vidybida et al (2005), Wang et al
(2005) and Fadel et al (2004), for the purpose of increasing
the sensitivities of their prototypes.
Figure 15. Noise from an integrated four-electrode structure: (a)
outer (current) electrodes, (b) inner (voltage) electrodes with current
and (c) inner electrodes without current (Kordas et al 1994).
(2005), they predicted a Lorentzian profile for the fluctuation
PSD.
Another work attempted to characterize the properties of
integrated micro-electrodes for a (CMOS) compatible medical
sensor (Kordas et al 1994). The thermal and excess noise of
the integrated electrodes was measured, similar to the approach
of Radhakrishnan and Lal (2003). Figure 15 shows the noise
characteristics of the micro-electrodes. The data obtained from
the measurements revealed several facts. First, the thermal
noise showed a frequency behavior following the impedance
characteristics of the electrodes. Second, excess noise due
to measuring current was much higher than without current,
and it also showed frequency dependence. Third, the sensor
performance was only affected by a small amount of thermal
noise. Finally, the excess noise did not occur at the sensing
electrodes.
Numerous studies were performed in the past few years
for the fabrication of DNA array chips. One of these (Li et al
2003) explored the need for a pre-hybridization step for DNA
detection to reduce background noise. Pre-hybridization is a
process where random DNA fragments are applied to coat the
chip surface after the probe attachment. This step is done to
reduce the background signal caused by nonspecific absorption
of target DNA and gold nanoparticles onto the entire surface
of the chip. The results showed that the current level from
the cell with DNA hybridization was almost equal without
and with pre-hybridization, but the current due to background
absorption was significantly reduced after a pre-hybridization
step. This work showed that the pre-hybridization step
increased the SNR of the chip and reduced the absorption
noise. Similar work was reported in Tu et al (2002).
In addition to these works, there were other studies
that examined the noise characteristics of biosensor designs,
namely those by Hagleitner et al (2002), Kim et al (2001),
Gupta et al (2004), Savran et al (2002, 2003) and Berney et al
(2000). In general, two noise sources account for the limited
performance of biosensors. The first one is the absorption and
desorption noise and the second source is electrical thermal
noise.
17. Biosensors
The same Stanford group, which proposed the electrical noise
model of electro-chemical sensors, published another work
to estimate the sensor inherent noise PSD of an affinitybased DNA sensor (Hassibi et al 2005). This project
involved determining the statistical behavior of affinity-based
biosensors. The noise originated from the probabilistic
molecular-level bindings within the sensing regions, as well
as the stochastic mass-transfer processes within the reaction
chamber. They modeled the dynamic behaviors of the sensor
by a Markov process by extracting the Markov parameters
from the reaction kinetic rates, diffusion coefficients and
reaction chamber boundary condition. Similar to Gomri et al
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18. Data storage devices
MEMS are expected to have a bright future for information
storage devices. A new technique, which is called ‘nanocuneiform’, is being explored by some companies for this
purpose. In this case, MEMS enable a new type of storage
technology. In addition, MEMS actuators are also being
considered for conventional magnetic drives to give finer
control of the read–write heads, which in turn decreases
the track spacing and increases storage density. In this
application, they can be part of magnetic disc systems,
extending their capabilities to higher densities. We review both
possibilities.
The new intrinsically MEMS storage technology is called
the ‘millipede’ by IBM, its developer (Eleftheriou et al 2003).
Electrostatic actuation is used to actively control the height
with respect to the planar data storage media of each probe
tip in a 32 by 32 array of AFM tips. Heat deforms the media
to provide a stored bit. Capacitive sensing is used to read out
bits from the media. The noise of the Millipede system is
composed of largely Johnson noise from the sensor and the
reference cantilever resistances, which reach a temperature of
350 ◦ C during the write operation, and from the low-pass filter
resistances, as well as noise from the operational amplifiers.
The SNR at the detection point due to these noise sources is
typically in the range of 16–20 dB.
Hitachi researchers presented a fast noise analysis of
thermal fluctuation noise on micromachined magnetoresistive
devices (van Peppen and Klaassen 2006). Normally, noise
analyses by micromagnetic simulations are computationally
very intensive and require enormous amounts of simulation
time. This paper presents a faster micromagnetic method to
arrive at the noise and small signal dynamics of these devices.
It showed the effect of spin torque transfer on the noise and
on the small signal dynamics of a current perpendicular to a
planar giant magnetoresistive (GMR) sensor. Further work
was performed on magnetic simulation of noise, SNR, and
bandwidth for the most common types of magnetic head:
tunneling magnetoresistive heads and GMR heads (Klaassen
et al 2006).
Carnegie Mellon University researchers presented a
standard system design consideration for magnetic storage
devices that employed MEMS devices for positioning of a
magnetic probe device over a magnetic media (Carley et al
2001). In this design, the electrostatic actuation and capacitive
sensing were used to actively control the height of each probe
tip, with respect to the media. It was found that the position
sensing circuit generated noise. This in turn limited the SNR
with which the Z separation between the media and the
probe tip could be controlled. Investigation revealed that the
dominant electronic noise source for the positive sense circuit
was the thermal noise of the MOS amplifier. In addition, there
were two other non-electronic noise sources in the system.
The first was the thermal vibration of air molecules and of
the molecules that make up the MEMS beams, namely the
Brownian noise. The second source, also significant, was
media noise, as is normally found in magnetic hard disk drives.
A sensitivity study for 40 Gb in−2 magnetic recording
systems on the fluctuations of head-disk spacing was
(a)
(b)
Figure 16. Relative noise power for transitions between bits in two
types of magnetic recording media for low (LC) and high (HC)
currents and head-disk spacings of 8 and 14 nm. The horizontal axis
is the distance along the recording direction (Yuan et al 1999).
reported by Yuan et al (1999).
The micromagnetic
simulation was carried out to obtain the behaviors of
two noise sources, transition noise and cross track noise.
The simulation considered two magnetic configurations of
recording systems, conventional longitudinal recording and
single layer perpendicular recording. The first part of the
work was to compute the transition noise. The results showed
that in the longitudinal recording media, there were no big
differences among the transition noises. However, higher
writing current and lower spacing caused the transition noise
to have a somewhat lower peak value. The simulations
using single layer perpendicular recording showed that the
transition noise was not sensitive to the spacing fluctuation
when high writing current was applied. The computations
further showed that, when a lower writing current was applied,
higher spacings had larger transition noise, and the noise
between the transitions increased drastically as the spacing
changed from 8 nm to 14 nm. Figure 16 shows the transition
noise profiles for both magnetic configurations. The second
part of the work attempted to characterize the cross track noise
for two magnetic configurations. The results of the simulations
show that higher writing current consistently produced bigger
track edge noise. Furthermore, both media were very sensitive
to the spacing fluctuations. The lower spacing produced more
cross track noise. However, single layer perpendicular media
with lower current writing generated more on-track noise as the
spacing was wider. This work proved that current selections
are crucial in reducing the noise sources in both types of
media.
There were other works that should be briefly mentioned.
One such work (El-Sayed and Carley 2002) attempted to
identify the noise sources on a 100 Gb in−2 magnetic-forcemicroscopy MEMS-actuated mass storage device, with a
follow-up paper three years later (El-Sayed and Carley 2005).
Chen et al (2001) and Igarashi et al (2003) attempted to
find the causes of instabilities in magneto-resistive recording
heads, and Pannetier et al (2005) investigated noise of GMR
sensors.
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Meas. Sci. Technol. 21 (2010) 012001
Topical Review
algorithms, techniques and computers are all available for
such works. Both Monte Carlo and molecular dynamic
computations should prove interesting and, possibly, useful
for the study of noise in MEMS, including the interactions of
various active mechanisms.
It is our hope that this review will provide a useful basis for
further research on noise in MEMS, both on fundamentals, and
on mechanisms and devices that have not been much studied to
date. The topic is as intellectually challenging as it is important
for MEMS employed in low-signal applications.
19. Magnetic MEMS
MEMS-based magnetic sensors are used for a wide range of
applications. Some of the designers performed noise studies
on their magnetic sensors. One group developed a magneticfield sensor that is based on an electron tunneling transducer
(DiLella et al 2000). The noise analysis was performed, and
it was found that the dominant source of the observed noise in
the device was low-frequency air pressure fluctuations.
There is also one noise study on another type of
magnetic sensor, called miniature fluxgate magnetometers
(Dimitropoulos 2005a, 2005b).
Several noise sources
of different origins have been found, namely (a) the
magnetic (Barkhausen) noise, (b) the noise superimposed
to the excitation waveform, (c) the noise generated due to
electromagnetic interference and (d) the noise generated due
to mechanical vibration of fluxgate cores. The various noise
sources have been modeled and their power spectral density
estimated from the experimental results. Similar work was
performed by Joisten et al (2004). The latest study reported
the dc and ac magnetic field dependence of the low-frequency
noise in a MEMS flux concentrator device containing a giant
magnetoresistance spin valve (Ozbay et al 2006, Edelstein
et al 2006).
Acknowledgments
Interest in and valuable comments on this work by Dr D S
Ong and Bassam Noaman are recalled with pleasure. Support
from Professor H T Chuah and from Professor A R Faidz is
also greatly appreciated.
Appendix. Units for noise
Units are utterly necessary in science, engineering and many
other fields, such as business (dollars, euros, pounds, etc).
They enable quantification of diverse parameters. But units
present two problems. The first challenge is to understand
them, both their definitions, plus whatever is part of the
definitions. For example, energy can be expressed as joules,
which are defined as the amount of energy expended when a
force of 1 N is applied over a distance of 1 m. The second
problem is conversion of units. Energy can be expressed by
any of several units, including electron volts, calories, ergs,
BTUs or quads. The numerical factors needed to convert from
one unit to another are diverse, but are readily available on
the Internet. Both of the general problems with units apply
to the units used to quantify various types of noise, which are
commonly frequency dependent.
The units used to express noise levels are independent
of the mechanisms that generate the noise. Of the many
units used to describe noise, probably the most physical and
understandable is noise power. It is frequency dependent, so a
graph of noise power as a function of frequency is commonly
called the power spectral density (PSD). The magnitude of
the PSD is the power within some small bandwidth (BW)
expressed in Hz. The absolute value of the PSD depends on
the BW, that is, there will be less power in a narrow spectral
region (BW) and vice versa.
The absolute value of the noise power can vary widely.
Hence, the noise power P is usefully expressed on a
logarithmic scale in decibels relative to a level of 1 mW, that
is, dBm. The noise power at some frequency for some BW
is given by the equation dBm = log10 (P/1 mW). This is the
quantity provided by many commercial spectral analyzers. If
the PSD is stationary, that is, if it is unvarying with time, then
the product of its value for any frequency interval, and the
length of some time interval of interest, gives the noise energy
in the particular bandwidth during that time period.
Other reference levels for noise in dB can be found. For
example, dBV are referred to 1 volt. dBU have a basis of
0.7746 volts. ‘U’ in dBU has various meanings, including
20. Conclusion
We pointed out the fundamental aspects of the different kinds
of noise mechanisms. Some experimental works have found
either electrical or non-electrical noise to be dominant. It is
critical for designers of MEMS, which will be used for lowsignal applications, to know the dominant noise mechanisms
in order to produce devices that will have lower noise from
those mechanisms.
We found that there are substantial works on noise in
MEMS, particularly in the area of modeling and measurements
of inertial MEMS and RF MEMS. The growing numbers of
noise studies in the area of optical, chemical and bio-MEMS
are noteworthy, as is the dearth of noise studies of MEMS
pressure sensors.
Different types of MEMS were found to have interesting
noise characteristics. For example, RF MEMS, especially
high-frequency resonators, are more susceptible to mechanical
noise than other classes of MEMS. While most of the effects
of noise on MEMS are undesirable, noise is exploited by
improved sensing in some chemical sensors. It seems possible
that the use of noise to determine the degradation of MEMS
over time and use will prove fruitful.
One of the attractive features of noise studies in MEMS
is the fact that the small sizes and masses of their parts can
bring both intrinsic electrical and non-electrical mechanisms
into play. Hence, there appears to be a need for theoretical and
experimental work on their interactions. Such research should
be more important for sensors and actuators with very small,
nano-scale components.
There is clearly much room for additional experimental
studies of noise in all types of MEMS. The same is true
of theoretical and computational studies. The equations,
17
Meas. Sci. Technol. 21 (2010) 012001
Topical Review
(a) unloaded source, (b) unspecified load impedance and (c)
unterminated.
For electrical noise, a basic relationship is used to describe
noise power P, namely P = V × I. The voltage V and current
I (in amperes) are related by Ohm’s law, V = I × R, where the
resistance R is expressed in ohms. Hence, P = V2 /R, as usual
within some BW in Hz. Because volts are a fundamental
unit in electrical engineering, it is common practice to take
the square root of the quantity V2 Hz−1 to get ‘volts per
root Hz’. Multiplicative factors, such as the resistance R,
can either be ignored or assumed to be the common value of
50 . Sometimes, the voltage is taken as the RMS (root mean
square) value, rather than the absolute value.
Volts per root Hz has the advantage of volts being very
a familiar unit. But the price for that convenience is having
to deal with the square root of the BW. While this is easy to
evaluate numerically, when the BW is known, it is very difficult
conceptually. It is neither physical nor easy to internalize,
when considering noise at different frequencies or in different
systems. That is, volts per root Hz does not refer to an actual
physical quantity for which a person can develop a feeling for
its magnitude. However unsavory is this unit, volts per root
Hz is now firmly established in reports on noise in electrical
systems. In fact, similar units are employed even when volts
are not involved. For example, ‘d per root Hz’ is used to
quantify noise in displacement (d) detection devices that sense
the position of a structure or object. Similarly, ‘g per root
Hz’ is employed for noise in accelerometers, where g is the
acceleration due to gravity at the surface of the earth. Figure
7 of this review gives an example of such units for MEMS
accelerometers.
The output of most MEMS devices is electrical, so that
it is common practice to express their noise in power as
dBm Hz−1 or in volts per root Hz. However, examination
of the experimental plots of noise as a function of frequency
in the figures of this paper shows that other noise units are
employed for MEMS involving electromagnetic energy, either
optical or radio frequency.
Micromachined optical sources include light emitting
diodes (LEDs), lasers (especially vertical cavity surface
emitting lasers, that is, VCSELs) and heated sources of
infrared radiation (notably micro-hotplates). The optical
beams emitted by these sources carry noise from various
mechanisms. MEMS optics include small mirrors and
diffraction elements, such as Fresnel lenses and gratings.
A few optical detectors qualify as MEMS, that is, they are
produced by micromachining processes. Both MEMS optics
and detectors can influence the relative intensity noise carried
by light in the visible and the nearby ultraviolet and infrared
spectral regions, and the signals that result from incidence of
these wavelengths on detectors.
The intensity of optical beams varies over time for a
variety of reasons, such as thermal instabilities, and pump
variations or cavity vibrations within lasers. The noise of
optical beams is often expressed as relative intensity noise
(RIN). This is the ratio of the noise, that is, the intensity
fluctuations, to the average intensity of the beam. RIN tends
to be independent of the absolute intensity. It varies with
frequency, and is commonly expressed as dB per Hz at a
specified frequency. Note that the intensity can be expressed
in units of quanta (photons) per second or energy per second
(power).
For radiation detectors that operate in the visible and
nearby spectral ranges, the noise-equivalent power (NEP) is
used to quantify the noise they introduce into a measurement.
The NEP is defined as the signal power that gives a signalto-noise ratio of unity for specific operating conditions.
Detectivity is defined as the reciprocal of the NEP. Hence,
detectors with low noise have high detectivity values. More
elaborate definitions of detectivity are often used. For example
D∗ (D-star) is the detectivity normalized to the area of a
detector and a unit bandwidth.
Many infrared, THz and microwave detectors are
bolometers, which work by responding to the temperature rise
due to absorption of radiation. In most cases, the temperature
of the scene being viewed by such detectors in systems is of
interest. Hence, a temperature-based unit is used to quantify
a detector or system noise. NETD stands for noise-equivalent
temperature difference. It is the change in the equivalent
blackbody temperature that gives a change in radiance onto
the detector and instrument that will give a signal-to-noise
ratio of unity. The NETD is above, but close to the limit
of detection for an optical sensor. The difference in scene
temperatures equal to the detector noise is called the Detector
NETD. The similar difference in scene temperature equal to
the system noise is the System NETD. The former is specific
to the detector and the latter includes system electronic noise.
We note in passing that sensors, other than those relying on
temperature rises, also have noise equivalents. For example,
pressure sensors have noise-equivalent pressures.
Phase noise is important in modern radio-frequency
communications and in a wide variety of digital systems. The
units used to quantify phase noise are not as widely understood
as are the units discussed above for quantifying the noise power
from various electrical or optical sources. Phase noise units are
critical to describing the performance of RF communication
systems, including RF MEMS, and the performance of digital
systems, including those that are part of MEMS devices. The
phase noise of an oscillator in an RF system is conceptually
related to the jitter in the clock in a digital system.
An understanding of phase noise can start with
consideration of a sine wave, which has three characteristics:
frequency, amplitude and phase. For a pure time-varying
sine wave, all of these quantities are constant. However, in
reality, they all have some associated noise. Variations in phase
produce deviations in the precise times at which the sine wave
is zero. These are equivalent to changes in frequency, which
is derived from the time between zero-crossings. Hence, in
the frequency domain, the spectrum of the wave is no longer
a delta function at the basic (carrier or clock) frequency, but
has a distribution around the fundamental frequency. This is
applicable to the phase variations of a sine wave (expressed
in degrees) and to the time jitter in an electrical, optical or
RF digital signal (given in seconds), which are related by the
equation
Jitter (s) = [Phase Error(◦ )]/[360 × Frequency (Hz)].
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Topical Review
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Figure A1. Drawing of the frequency spectrum due to phase noise
on a carrier at fc (from Wikipedia).
The frequency distribution has a width determined by the
magnitude of the phase noise. The frequency-dependent
amplitude of the phase noise is determined by the details of
the source of phase noise. The schematic in figure A1 shows
the PSD, written as SC (f ), for the carrier and the associated
distribution due to phase noise. The phase noise spectrum is
L(f – fc ), which is referenced to the amplitude of the spectrum
at the carrier frequency. The phase noise spectrum is expressed
as dBc, that is, decibels relative to the carrier. It is the
frequency-dependent power ratio of the phase noise relative
to the power of the carrier. The mathematical definition of
phase noise is
L(f − fc ) = 10 log[Sc (f )/Sc (fc )]
in dBc.
That is, rather than being referenced to an absolute quantity
like milliwatts (for dBm), the phase noise PSD is referenced
to the carrier power that exists for a particular situation.
As is usual for a PSD, the magnitude in dBc for phase
noise is actually referenced to a particular bandwidth since the
absolute value will depend on the BW used to measure the
phase noise PSD. That is, the units are actually dBc Hz−1 . As
with the units discussed above, (power/frequency) has units
of (energy/time)/(1/time) or energy.
It must be noted that there are MEMS sources of radio
frequencies, specifically oscillators of several types. The
units of dBc or dBc Hz−1 apply to such oscillators. Further,
other MEMS RF devices, such as switches and RF detectors,
can increase or otherwise modify the noise in RF signals
propagating through them.
The conversion of noise units from one basis to another
is sometimes desirable. For example, the power in an optical
or RF electromagnetic beam can be expressed equally as the
number of quanta (photons) passing per unit of time, or in
more common power (energy per time) units.
In summary, the quantitative expression of noise power
is generally done relative to an absolute value (commonly
1 mW) for electrical signals, relative to the average power
for optical signals, or relative to the power of the carrier
for radio-frequency signals. These do not cover all cases,
for example, noise in acoustic signals (given as the
sound power level), or electrostatic or magnetostatic signals
(expressed as field strengths). However, an appreciation of
noise units for electrical and electromagnetic signals does
cover most of the cases for MEMS and other small devices.
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