INV ITEDP A P E R
Review: SemiconductorPiezoresistance forMicrosystemsThis paper provides a comprehensive overview of integrated piezoresistor technology
with an introduction to the physics of piezoresistivity, process and material
selection and design guidance useful to researchers and device engineers.
By A. Alvin Barlian, Woo-Tae Park, Joseph R. Mallon, Jr.,
Ali J. Rastegar, and Beth L. Pruitt
ABSTRACT | Piezoresistive sensors are among the earliest
micromachined silicon devices. The need for smaller, less
expensive, higher performance sensors helped drive early
micromachining technology, a precursor to microsystems or
microelectromechanical systems (MEMS). The effect of stress
on doped silicon and germanium has been known since the
work of Smith at Bell Laboratories in 1954. Since then,
researchers have extensively reported on microscale, piezo-
resistive strain gauges, pressure sensors, accelerometers, and
cantilever force/displacement sensors, including many com-
mercially successful devices. In this paper, we review the
history of piezoresistance, its physics and related fabrication
techniques. We also discuss electrical noise in piezoresistors,
device examples and design considerations, and alternative
materials. This paper provides a comprehensive overview of
integrated piezoresistor technology with an introduction to the
physics of piezoresistivity, process and material selection and
design guidance useful to researchers and device engineers.
KEYWORDS | MEMS; microfabrication; micromachining; micro-
sensors; piezoresistance; piezoresistor; sensors
I . INTRODUCTION
Piezoresistive sensors are among the first Micro-Electro-
Mechanical-Systems (MEMS) devices and comprise a
substantial market share of MEMS sensors in the market
today [1], [2]. Silicon piezoresistance has been widely used
for various sensors including pressure sensors, accelerom-
eters, cantilever force sensors, inertial sensors, and strain
gauges. This paper reviews the background of semicon-
ductor piezoresistor research (Section I), physics and limi-
tations (Section II), applications and devices (Section III),
and newer promising piezoresistive materials (Section IV).
A. HistoryWilliam Thomson (Lord Kelvin) first reported on the
change in resistance with elongation in iron and copper
in 1856 [3]. Telegraph wire signal propagation changes
and time-related conductivity changes, nuisances to tele-
graph companies, motivated further observations of con-
ductivity under strain. In his classic Bakerian lecture to
the Royal Society of London, Kelvin reported an elegant
experiment where joined, parallel lengths of copper and
iron wires were stretched with a weight and the dif-ference in their resistance change was measured with a
modified Wheatstone bridge. Kelvin determined that, since
the elongation was the same for both wires, ‘‘the effect
observed depends truly on variations in their conductivi-
ties.’’ Observation of these differences was remarkable,
given the precision of available instrumentation.
Motivated by Lord Kelvin’s work, Tomlinson con-
firmed this strain-induced change in conductivity andmade measurements of temperature and direction depen-
dent elasticity and conductivity of metals under varied
orientations of mechanical loads and electrical currents
(Fig. 1) [4], [5].
The steady state displacement measurement tech-
niques of Thomson and Tomlinson were replicated, refined,
and applied to other polycrystalline and amorphous
Manuscript received May 2, 2008; revised October 6, 2008. Current version published
April 1, 2009. Research in the Pruitt Microsystems Laboratory related to
piezoresistance has been supported by the National Science Foundation under awards
ECCS-0708031, ECS-0449400, CTS-0428889, ECS-0425914, and PHY-0425897 and the
National Institutes of Health under award R01 EB006745-01A1.
The authors are with Stanford University, Mechanical Engineering, Stanford,
CA 94305 USA (e-mail: [emailprotected]; [emailprotected];
[emailprotected]; [emailprotected]; [emailprotected]).
Digital Object Identifier: 10.1109/JPROC.2009.2013612
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 5130018-9219/$25.00 �2009 IEEE
conductors by several researchers [6]–[9]. In 1930, Rolnick
presented a dynamic technique to quantify the resistance
change in vibrating wires of 15 different metals [10]. In 1932,Allen presented the first measurements of direction-dependent conductivity with strain in single crystals of
bismuth, antimony, cadmium, zinc and tin [11]–[14]. Based
on her work, Bridgman developed a tensor formulation for
the general case of hom*ogeneous mechanical stress on the
electrical resistance of single crystals [6], [7].
In 1935, Cookson first applied the term piezoresistance
to the change in conductivity with stress, as distinctfrom the total fractional change of resistance [15]. The
term was most likely coined after piezoelectricity, the
generation of charge with applied stress, a ferroelectric-
mediated effect quite different from piezoresistivity.
Hanke coined the term piezoelectricity in 1881 after
Fpiezen_ from the Greek to press [16], [17]. The now stan-
dard notation for piezoresistivity was adapted from
analogous work on piezoelectricity [18]. Voigt formalizedtensor notation for stress and strain in crystals and for-
mulated tensor expressions for generalized Hooke’s Law
and piezoelectricity [19]. He adapted this notation from
the works of Curie and Kelvin [18], [20]–[23].
In 1938, more than 80 years after the discovery of
piezoresistance, Clark and Datwyler used a bonded wire
to monitor strain in a stressed member [24]. In the same
year, Arthur Ruge independently reinvented the bondedmetallic strain gauge which had been first suggested by
Edward Simmons, Jr. in 1936 [25]–[28].
In 1950, Bardeen and Shockley predicted relativelylarge conductivity changes with deformation in single
crystal semiconductors [29]. In his seminal paper on semi-
conductor piezoresistance, C. S. Smith (a researcher who
was visiting Bell Laboratories from Case Western Reserve
University and who was interested in anisotropic electrical
properties of materials), reported the first measurements
of the Fexceptionally large_ piezoresistive shear coefficient
in silicon and germanium [30].In 1957, Mason and Thurston first reported silicon
strain gauges for measuring displacement, force, and
torque [31]. Semiconductor strain gauges, with sensitivity
more than fifty times higher than conventional metal
strain gauges, were considered a leap forward in sensing
technology. Early silicon strain gauges were fabricated by
sawing and chemical etching to form a Fbar_ shaped strain
gauge [32]. The gage was then attached to a materialsurface with cement. This method allowed the develop-
ment of the first bonded semiconductor pressure sensors.
The first commercial piezoresistive silicon strain gauges
and pressure sensors started to appear in the late 1950’s.
Kulite Semiconductor, founded in 1958 to exploit piezo-
resistive technology, became the first licensee under the
Bell piezoresistive patents [33]. By 1960 there were at least
two commercial suppliers of bulk silicon strain gauges:Kulite-Bytrex and Microsystems [33]. Fig. 2 shows modern
bar and U-shaped silicon strain gauges.
Developments in the manufacture of semiconductors,
especially ho*rni’s invention of the Fplanar_ transistor in
1959, resulted in improved methods of manufacturing
piezoresistive sensors [34]. Silicon piezoresistive devices
evolved from bonded single strain gauges to sensing devices
Fig. 1. The alteration of specific resistance produced in different
metals by hammering-induced strain. After Tomlinson, 1883 [5].
Reprinted with permission from the Royal Society Publishing.
Fig. 2. Modern micromachined, precision-etched silicon gages with
welded lead wires. (a) Bar shaped strain gauge with a length of 6 mm.
(b) U-shaped strain gauge with a length of 1.2 mm. Courtesy of
Herb Chelner, Micron Instruments, Simi Valley, CA.
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
514 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
with ‘‘integrated’’ (in the sense that the piezoresistiveregion was co-fabricated with the force collector) piezo-
resistive regions. In their classic 1961 paper, Pfann and
Thurston proposed the integration of diffused piezo-
resistive elements with a silicon force collecting element
[35]. The first such Fintegrated_ device, a diffused piezo-
resistive pressure sensing diaphragm was realized by
Tufte et al. at Honeywell Research in 1962 [36].
Piezoresistive sensors were the first commercialdevices requiring three-dimensional micromachining of
silicon. Consequently, this technology was a singularly
important precursor to the MEMS technology that
emerged in the 1980’s. In 1982, Petersen’s seminal paper
‘‘Silicon as a Mechanical Material’’ reviewed several
micromachined silicon transducers, including piezoresis-
tive devices, and the fabrication processes and techniques
used to create them [37]. Petersen’s paper helped drive thegrowth in innovation and design of micromachined silicon
devices over the subsequent years.
The field benefited, to a degree that no other sensor
technology has, from developments in silicon processing
and modeling for the integrated circuits (IC) industry.
Technological advances in the fabrication of ICs including
doping, etching, and thin film deposition methods, have
allowed significant improvements in piezoresistive devicesensitivity, resolution, bandwidth, and miniaturization
(Fig. 3). Reviews of advances in MEMS, microstructures,
and microsystems are available elsewhere [38], [39].
II . PIEZORESISTANCE FUNDAMENTALS
The electrical resistance ðRÞ of a hom*ogeneous structure is
a function of its dimensions and resistivity ð�Þ,
R ¼ �l
a; (1)
where l is length, and a is average cross-sectional area. Thechange in resistance due to applied stress is a function of
geometry and resistivity changes. The cross-sectional area
of a bulk material reduces in proportion to the longitudinal
strain by its Poisson’s ratio, �, which for most metals ranges
from 0.20 to 0.35. For anisotropic silicon, the effective
directional Poisson’s ratio ranges from 0.06 to 0.36 [40],
[41]. The isotropic lower and upper limit for � are�1.0 and
0.5 [42].The gauge factor ðGFÞ of a strain gauge is defined as
GF ¼ �R=R
"(2)
where " is strain and �R=R is fractional resistance change
with strain. The change in resistance is due to both the
geometric effects ð1þ 2�Þ and the fractional change inresistivity ð��=�Þ of the material with strain [10],
�R
R¼ ð1þ 2�Þ"þ��
�: (3)
Geometric effects alone provide a GF of approximately 1.4to 2.0, and the change in resistivity, ��=�, for a metal is
smallVon the order of 0.3. However, for silicon and
germanium in certain directions, ��=� is 50–100 times
larger than the geometric term. For a semiconductor,
elasticity and piezoresistivity are direction-dependent
under specified directions of loads (stress, strain) and
fields (potentials, currents). This section first reviews
notation and then discusses fundamentals of piezoresis-tivity in semiconductors. We also refer the reader to the
comprehensive background on piezoelectricity in Nathan
and Baltes [43].
Fig. 3. Technological advances in IC fabrication (above the horizontal line) and micromachining (below the horizontal line)
[30], [33]–[37], [47], [79], [112], [122], [130], [149], [160], [191], [251], [254], [268], [284], [372]–[384].
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 515
A. Notation
1) Miller Indices and Crystal Structure: Crystals have
periodic arrangements of atoms arranged in one of 14 lattice
types and complete reviews are available elsewhere [44],
[45]. The Miller indices specify crystal planes by n-tuples. A
direction index ½hkl� denotes a vector normal to a plane
described by ðhklÞ, and t represents a family of planes
equivalent to ðhklÞ by symmetry. Angle-bracketed indices,like hhkli, represent all directions equivalent to ½hkl� by
symmetry. In a hexagonal crystal, as found in most silicon
carbide polytypes, the Bravais-Miller index scheme is
commonly adopted where four indices are used to represent
the intercept-reciprocals corresponding to the four principal
crystal axes (a1, a2, a3, and c). The axes a1, a2, and a3 are on
the same plane and 120� apart from one another while c is
perpendicular to the a-plane defined by the (a1, a2, a3) triplet.Crystalline silicon forms a covalently bonded diamond-
cubic structure with lattice constant a ¼ 5.43 A [Fig. 4(a)].
The diamond-cubic structure is equivalent to two inter-
penetrating face-centered-cubic (FCC) lattices with basis
atoms offset by 1=4a in the three orthogonal directions [44].
Silicon’s diamond-cubic lattice is relatively sparse (34%
packing density) compared to a regular face-centered-cubic
(FCC) lattice (74% packing density). Commonly used wafersurface orientations in micromachining include (100), (111),
and (110) [Fig. 4(b)]. Photolithography and etch techniques
can create devices in various directions to access desirable
material properties. For instance a h111i oriented piezo-
resistor in a (110) plane will have the highest piezoresistive
sensitivity in a pressure sensor [46]. More commonly h110ialigned piezoresistors on (100) wafers are used because of
their high equal and opposite longitudinal and transversepiezoresistive coefficients. Directionality of silicon piezo-
resistive coefficients is discussed in Sections II-A3 and
II-D1, and the selection of device orientation with direc-
tional dependence is discussed in more detail elsewhere
[31], [35], [47], [48].
2) Stress, Strain, and Tensors: To define the state of stress
for a unit element (Fig. 5), nine components, �ij, must bespecified, as in:
� ¼�11 �12 �13
�21 �22 �23
�31 �32 �33
66647775: (4)
The first index i denotes the direction of the applied stress,
while j indicates the direction of the force or stress. If
i ¼ j, the stress is normal to the specified surface, while
i 6¼ j indicates a shear stress on face i (Fig. 5). From staticequilibrium requirements that forces and moments sum to
zero, a stress tensor is always symmetric, that is �ij ¼ �ji,
and thus the stress tensor contains only six independent
components. Strain, "ij, is also directional. For an isotropic,
Fig. 4. (a) Covalently bonded diamond cubic structure of silicon.
(b) Commonly employed crystal planes of silicon, i.e., (100), (110), and
(111) planes. Silicon has four covalent bonds and coordinates itself
tetrahedrally. The {111} planes, oriented 54.74� from {100} planes, are
most densely packed. Mechanical and electrical properties vary greatly
with direction, especially between the most dense {111} and the least
dense {100} planes.
Fig. 5. Nine components, �ij, of stress on an infinitesimal unit element.
For clarity, stresses on negative faces are not depicted.
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
516 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
hom*ogeneous material, stress is related to strain byHooke’s Law, � ¼ "E [49].
Although ‘‘effective’’ values of Young’s modulus and
Poisson’s ratio for a single direction are often employed for
simple loading situations, a tensor is required to fully
describe the stiffness of an anisotropic material such as
silicon [37], [50], [51]. The stress and strain are related by
the elastic stiffness matrix, C, where �ij ¼ Cijkl � "kl, or
equivalently by the inverse compliance matrix, S, where"ij ¼ Sijkl � �kl:
�11
�22
�33
�23
�13
�12
2666666664
3777777775¼
c11 c12 c13 c14 c15 c16
c12 c22 c23 c24 c25 c26
c13 c23 c33 c34 c35 c36
c14 c24 c34 c44 c45 c46
c15 c25 c35 c45 c55 c56
c16 c26 c36 c46 c56 c66
2666666664
3777777775
"11
"22
"33
2"23
2"13
2"12
2666666664
3777777775
(5)
"11
"22
"33
2"23
2"13
2"12
2666666664
3777777775¼
s11 s12 s13 s14 s15 s16
s12 s22 s23 s24 s25 s26
s13 s23 s33 s34 s35 s36
s14 s24 s34 s44 s45 s46
s15 s25 s35 s45 s55 s56
s16 s26 s36 s46 s56 s66
2666666664
3777777775
�11
�22
�33
�23
�13
�12
2666666664
3777777775: (6)
Collapsed notation reduces each pair of subscripts to one
number: 11!1, 22!2, 33!3, 23!4, 13!5, 12!6,
e.g., �11 to �1, "12 to "6, c1111 to c11 and s2323 to s44.
3) Piezoresistance: Single crystal germanium and silicon,both of which have a diamond lattice crystal structure,
were the first materials widely used as piezoresistors.
Smith reported the first measurements of large piezo-
resistive coefficients in these semiconductor crystals in
1954 noting that work by Bardeen and Shockley, and later
Herring, could explain the phenomena [30]. Smith applied
Bridgman’s tensor notation [8] in defining the piezo-
resistive coefficients and geometry of his test configura-tions (Fig. 6). The piezoresistive coefficients ð�Þ require
four subscripts because they relate two second-rank
tensors of stress and resistivity. The first subscript refers
to the electric field component (measured potential), the
second to the current density (current), and the third and
fourth to the stress (stress has two directional compo-
nents). For conciseness, the subscripts of each tensor are
also collapsed [31], e.g., �1111 ! �11, �1122 ! �12,�2323 ! �44. Kanda later generalized these relations for
a fixed voltage and current orientation ð!Þ as a function of
stress ð�Þ [47]:
��!�¼X6
�¼1
�!���: (7)
Smith determined these coefficients for relatively lightlydoped silicon and germanium samples with resistivities
ranging from 1.5–22.7 �-cm, e.g., 7.8 �-cm for p-type
silicon [30]. Current commercial and research practice
uses doping levels several orders of magnitude higher than
Fig. 6. Notation for Smith’s test configurations. Configurations A and C measured longitudinal piezoresistance, while configurations B and D
provided transverse coefficients. Voltage drops between the electrodes (dotted lines) were measured while uniaxial tensile stress, �, was applied
to the test sample by hanging a weight. The experiments were done in constant-current mode in a light-tight enclosure with controlled
temperature ð25� 1 �CÞ. After Smith [30]. � 1954 American Physical Society, http://www.prola.aps.org/abstract/PR/v94/i1/p42_1.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 517
Smith’s. Higher concentrations have somewhat lowerpiezoresistive coefficients, but much lower temperature
coefficients of resistance and sensitivity. For example, in
our laboratory, we regularly use doping levels that result in
resistivities in the range of 0.005–0.2 �-cm [52]–[57].
Smith measured the piezoresistive coefficients for (100)
samples along the h100i and h110i crystal directions. Lon-
gitudinal and transverse coefficients for the fundamental
crystal axes were determined directly. Shear piezoresistivecoefficients were inferred. By these measurements and
considering the crystal symmetry, Smith fully character-
ized the piezoresistive tensor of 7.8 �-cm silicon as
½�!�� ¼
�11 �12 �12 0 0 0
�12 �22 �12 0 0 0
�12 �12 �33 0 0 0
0 0 0 �44 0 0
0 0 0 0 �44 0
0 0 0 0 0 �44
2666666664
3777777775
¼
6:6 �1:1 �1:1 0 0 0
�1:1 6:6 �1:1 0 0 0
�1:1 �1:1 6:6 0 0 0
0 0 0 138:1 0 0
0 0 0 0 138:1 0
0 0 0 0 0 138:1
2666666664
3777777775
� 10�11 Pa�1: (8)
In another early paper, Mason and Thurston utilizedbonded gauges with the most favorable longitudinal orien-
tations to measure displacement, force, and torque [31].
They derived directional coefficients from full formu-
lations relating the electric field, current density, and
stress components. They also presented more general for-
mulations for longitudinal ð�011Þ and transverse ð�012Þpiezoresistive coefficients for a gauge in an arbitrary crys-
tal direction,
�011 ¼ �11 � 2ð�11 � �12 � �44Þ� l21 m2
1 þ l21 n21 þ m2
1 n21
� �; (9)
and
�012 ¼ �120 þ 2ð�11 � �12 � �44Þ� l21 l22 þ m2
1 m21 þ n2
1 n22
� �; (10)
where l, m, and n are the direction cosines of the direction
associated with �011 or �012, with respect to the crystallo-
graphic axes.
Pfann and Thurston [35] recognized the benefits of
using transverse and shear piezoresistance effects inconjunction with longitudinal piezoresistance for devices.
Many of their geometries employed a full Wheatstone
bridge with two longitudinal and two transverse piezo-resistors to increase sensitivity and compensate for resis-
tance changes due to temperature (Sections II-D2 and
III-E). Notably, they proposed integrating the piezo-
resistors with the force collecting structure and discussed
the advantages and disadvantages of a number of geo-
metries for various types of measurements. They antic-
ipated most of the geometries widely employed today.
Stress sensitivity in silicon also can be exploited by thepseudo-Hall effect and the piezojunction effect. The pseudo-
Hall effect is based on the shear piezoresistive effect,
whereby the induced shear stress distorts the potential
distribution in a piezoresistive plane. Motorola Semicon-
ductor (now Freescale Semiconductor) used this configu-
ration in a pressure sensor in the 1970s [58] and has
continued producing this type of pressure sensor.
Doelle et al. and Gieschke et al. reported geometry-baseddesign rules and novel applications for the pseudo-Hall
effect piezoresistive plates [59]–[61]. The piezojunction
effect is defined as the change in the saturation current of a
bipolar transistor or a p-n junction due to mechanical stress
[62]. Metal-oxide-semiconductor field effect transistors
(MOSFETs) using the piezojunction effect have been
demonstrated for small cantilever strain sensing [63]–[65].
The main advantage over conventional piezoresistors lies inreduced power consumption but this trades off with size
and circuit complexity [66]. The piezojunction effect is also
important to understanding sources of unwanted offset in
integrated circuits and sensors [67]–[70].
B. Piezoresistive TheoryThe discovery of such large piezoresistive effects
demanded a theory of the underlying physics. This sectiondiscusses the prevailing theories at the time of Smith’s
measurements as well as more recent advances. The the-
ories of semiconductor piezoresistance are grounded in
one-dimensional descriptions of electron and hole trans-
port in crystalline structures under strain (potentially
extended to three dimensions and to include crystal
defects, electric potentials, and temperature effects). The
various models require some framework of bandgap energymodels, wave mechanics, and quantum effects; the
interested reader is referred to [44], [71]–[73] and the
references of this section for more information.
At the time of Smith’s piezoresistance measurements,
existing theories were based on shifts in bandgap energies.
The band structure of diamond (Fig. 7) was first calculated
by Kimball in 1935 [74], and that of silicon by Mullaney in
1944 [75]. In 1950, Bardeen and Shockley presented amodel for mobility changes in semiconductors subjected to
deformation potentials and compared both predicted and
measured conductivity changes in the bandgap with di-
lation [29]. This work served as the basis for later analyses,
such as that of Herring [76], [77] and Long [78].
The mobilities and effective masses of the carriers are
significantly different from one another and fluctuate under
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
518 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
strain. N- and p-type piezoresistors exhibit opposite trends
in resistance change and different direction-dependent
magnitudes under stress. The magnitudes and signs of the
piezoresistive coefficients depend on a number of factorsincluding impurity concentration, temperature, crystallo-
graphic direction, as well as the relation of voltage, current
and stress to one another and to the crystallographic axes.
The relationship between carrier characteristics and strain
has been investigated both experimentally [30], [31], [79]
and analytically [29], [35], [47], [77], [80], [81]. Focusing on
n-type silicon, these early studies utilized either effective
mass or energy band calculations with wave propagation inone direction at a time. The change in mobility (and thus,
conductivity) with lattice strain is attributed to band
warping or bending and the non-uniform density of states.
The implications for the related large mobility and resis-
tance changes were not realized prior to Smith’s discovery
[82], [83]. Following Bardeen and Shockley’s models for
mobility changes with deformation potentials, more refined
models of transport and energy band structure based onnew experimental work became available. In 1955, Herring
proposed his Many-Valley model, which adequately ex-
plained piezoresistance for n-type silicon and germanium
[29], [35], [77], [80], [81], [84]–[87].
Herring’s Many-Valley model for n-type silicon pro-
poses three symmetrical valleys along the h100i direction
[77]. His model projects the band energy minima in three
orthogonal directions ðx; y; zÞ as locations of constantminimum energy (Fig. 8). The minimum energy of each
valley lies along the centerline of the constant energy
ellipsoid of revolution. Electrons have a higher mobility
along the direction perpendicular to the long axis of the
ellipsoid. Since electrons occupy lower energy states first,
they are found in these regions bounded by ellipsoids of
constant low-energy. These ellipsoids, bounded by higher-
energy regions, are referred to as valleys. With strainhowever, the symmetry is broken and the ellipsoids are
asymmetrically dilated or constricted. This results in an
anisotropic change in conductivity proportional to strain.
Most models represent the direction dependence of
bandgap and electron energies by either directional waves
(k has direction and magnitude) or momentum ðpÞ and the
effective masses of the carriers. The energy surfaces for
electron mobility are accordingly represented in k-space ormomentum space. The wave propagation is confined to
Fig. 7. Energy bands split in diamond and are a function of strain or
atomic spacing, R (Atomic Units). Besides the four shaded bands, there
are four bands of zero width, i.e. two following curve IV and two
following curve VI. After Kimball [74]. � 1935 American Institute of
Physics.
Fig. 8. (a, b) Test configuration and resulting schematic diagrams of probable constant energy surfaces in momentum space for n-type Si with
potential, E, and strain, e, as depicted. The electrons are located in six energy valleys at the centers of the constant energy ellipses, which are
shown greatly enlarged. The effect of stress on the two valley energies shown is indicated by the dotted ellipsoids. The mobilities, �, of the
several groups of charge carriers in various directions are roughly indicated by the arrows. The test configurations correspond to Smith’s
experimental arrangements A and C (Fig. 6). After Smith [30]. � 1954 American Physical Society. (c) The changes in silicon energy minima with
dilation in a plane normal to a (001) axis. Four minima vary as shown by the solid line, and two on the axis normal to the plane follow the dashed
line. After Keyes [87], � 2002 IEEE.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 519
quantum states by the periodicity of the lattice, and edgesin the band diagrams correspond to the edges of the
Brillouin zone (smallest primitive cell, or unit cell, of the
reciprocal lattice) oriented in a direction of interest [44].
In the unstrained silicon crystal, the lowest conduction
band energies (valleys) or highest mobility orientations are
aligned with the h100i directions. The conduction
electrons are thus imagined to be lying in six equal groups
or valleys, aligned with three h100i directions. For anyvalley, the mobility is the lowest when parallel to the valley
direction, and the highest when perpendicular to the valley,
e.g., an electron in the z valley has higher mobility in the xand y directions. Net electron conductivity is the sum of the
conductivity components along the three valley orienta-
tions and is independent of direction. Net mobility is the
average mobility along the three valleys (two high and one
low) [87]. Uniaxial elongation increases the band energy ofthe valley parallel to the strain and transfers electrons to
perpendicular valleys, which also have high mobility along
the direction of strain. Electrons favor transport in
directions of higher mobility (higher conductivity and
lower resistance) in the direction of strain, and tension
removes electrons from the valley in that direction and
transfers them to valleys normal to the tension. In n-type
silicon, average mobility is increased in the direction oftension (longitudinal effect) and lowered transverse to that
direction (transverse effect). Compression has the opposite
effect. Lin later provided an explanation of large mobility
degradation at higher transverse electric fields and lower
temperatures based on the physics of electron population
and scattering mechanisms of quantized subbands at (100)
Si surfaces [88].
The piezoresistance theory for n-type semiconductorscontinued to be refined from 1954 onward, but until
recently ‘‘piezoresistive effects in p-type silicon have not
been fully clarified due to the complexity of the valence
band structure’’ [89]. In 1993, Ohmura stated that ‘‘the
[piezoresistance] effect for n-type Ge and Si has been
successfully accounted for. . .’’ while ‘‘the [piezoresistance]
effect for p-type Si and Ge has not been fully under-
stood. . .’’ [90]. However, recent computational advanceshave enabled an improved understanding of p-type piezo-
resistance [73], [91]–[93]. This is important because most
research and commercial piezoresistive devices are p-type
and models of this successful technology had been largely
based on empirical results. Theoretical studies based on the
strain Hamiltonian [94]–[96] and on deformation poten-
tials in strained silicon as well as cyclotron resonance
experimental results have revealed several factors thataffect hole mobilities in semiconductors, e.g., band warp-
ing and splitting, mass change, etc. [97]–[101].
Historically, piezoresistive technology drew from main-
stream IC research and continues to do so. Now, with the
strong interest in ‘‘strain engineering’’ to increase transport
speed in ICs, the situation has reversed and mainstream
semiconductor technology is drawing on findings of piezo-
resistive research. Strain engineered materials (e.g., inclu-
sion of germanium into a silicon layer) can increase themobility of a channel in MOS (metal-oxide-semiconductor)
devices [73], [102]–[104]. Suthram et al. [104] applied large
uniaxial stress on n-type MOS field-effect transistors
(MOSFETs) and showed that piezoresistive coefficients
were constant while the electron mobility enhancement
increased linearly for stresses up to �1.5 GPa. Fig. 9 shows
plotted hole mobility enhancement factor for several
semiconductors as a function of stress.
C. Piezoresistor FabricationSeveral design and process parameters such as energy,
dose and doping method as well as anneal parameters such
as temperature, time and environment affect piezoresistor
sensitivity and noise. We review the commonly used
fabrication methods for forming piezoresistors on semi-
conductor substrates and discuss their advantages anddrawbacks. Diffusion, ion implantation, and epitaxy are
the most common impurity-doping techniques for intro-
ducing dopants into a silicon substrate. These techniques
result in different doping profiles (Fig. 10). A complete
review of doping techniques is available elsewhere [105].
1) Diffusion: Diffusion is the migration of dopant atoms
from a region of high concentration to a region of low
concentration. The fabrication of piezoresistors usingdiffusion involves a pre-deposition and a drive-in step.
Fig. 9. Hole mobility enhancement in semiconductors, taking into
account surface roughness scattering, as a function of stress (�GPa).
Sun et al. compared their experimental results with those of several
groups [385]–[387] and noted that ‘‘the hole mobilities of Ge and GaAs
increase steadily with stress up to 4 GPa, while the hole mobility of
Si saturates at about 2 GPa. For the technologically important stresses
of 1-2 GPa, Ge shows similar enhancement as Si. However the
unstressed hole mobility of Ge is�3� higher than Si.’’ Reprinted with
permission from Sun [73], � 2007 American Institute of Physics.
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520 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
During the pre-deposition step, wafers may be placed in a
high-temperature furnace (900–1300 �C) with a gas-phaseor a solid-phase dopant source [105], [106]. The gas-phase
dopant source, e.g., diborane (B2H6), phosphine (PH3), or
arsine (AsH3), is carried in an inert gas, e.g., N2 or Ar. The
solid-phase dopant source (a compound containing dopant
atoms in a form of solid discs) is placed such that the active
surface is facing the surface of the silicon wafer inside the
furnace. Both the source and the wafer are heated, causing
transport of dopants from the source to the wafer. Alter-nately, dopant pre-deposition may utilize doped spin-on
glass layers [107]–[109]. During pre-deposition, the
boundary condition is a constant surface concentration
and the doping profile is approximated by a complemen-
tary error function. The source can be removed and
dopants ‘‘driven-in’’ deeper with high temperature anneal-
ing (900–1300 �C). Gas-phase dopant sources provide
inconsistent doses for surface concentrations below thesolid solubility level.
2) Ion Implantation: Ion implantation was researched
extensively in the 1950s and 1960s as an alternate pre-
deposition method to provide better control of the dopant
dose [105], [110]–[121]. Ion implantation gained wide use
in the 1980s and remains the preferred method today. In
ion implantation, dopant ions are accelerated at highenergy (keV to MeV) into the substrate. The ions leave a
cascade of damage in the crystal structure of the implanted
substrate [118]. Any layer thick or dense enough to block the
implanted ions, such as photoresist, silicon oxide, silicon
nitride, or metal, can be used for masking. Typical silicon
piezoresistor doses range from ð1� 1014 to 5� 1016 cm�2,
with energy ranges from 30 to 150 keV [51]. Dopant
distribution is approximated by a symmetric Gaussiandistribution (Fig. 10). Most implants are done with a 7�
tilt of (100) silicon wafers to avoid ion channeling, a
phenomenon where ions deeply traverse gaps in the lattice
without scattering. Larger implant angles (7�–45�) are
sometimes used to form piezoresistors on etched sidewalls of
deep-reactive-ion-etched (DRIE) trenches as found inflexures or beams in dual-axis cantilevers, in-plane accel-
erometers, and shear stress sensors [53], [122]–[125]. One
major disadvantage of ion implantation is significant damage
to the crystal. Lattice order is mostly restored by high-
temperature dopant activation and annealing [118]. How-
ever, shallow junctions are difficult to obtain with high
crystal quality. Parameters that affect the junction depth
include the acceleration energy, the ion mass, and thestopping power of the material [115].
3) Epitaxy: Epitaxy is the growth of atomic layers on
single-crystal materials that conform to the crystal-
structure arrangement on the surface of the crystalline
substrate [105]. Chemical Vapor Deposition (CVD) tech-
nique can be used to deposit epitaxial silicon by decom-
posing silane (SiH4) or by reacting silicon chloride (SiCl4)with hydrogen. Conventional epitaxial growth is done at
high temperatures (1000–1250 �C) and reduced pressure
(30–200 torr). A clean surface is necessary to obtain a high
quality epitaxial layer. Contaminants and native oxide will
prevent single-crystal growth. An in situ HCl clean can
remove wafer contaminants and native oxide. Halide
source gases, such as SiCl4, SiHCl3, or SiH2Cl2 (DCS),
are used to grow silicon with the advantage that chlorine isone of the net byproducts. The chlorine removes metal
contaminants from the deposited silicon film, resulting in
better quality single-crystal silicon. Selective deposition of
epitaxial silicon, i.e., the silicon deposits only on exposed
regions of silicon, but not on other dielectric films such as
SiO2 or Si3N4, can be achieved by tailoring the deposition
conditions [55], [105], [126]–[129]. Epitaxial silicon films
may be doped during the deposition by introducing ap-propriate dopant source gases such as AsH3, PH3, or B2H6
into the chamber along with the silicon source gases.
Epitaxial piezoresistors require no annealing and have
a uniform dopant profile (Fig. 10). Epitaxy has enabled
Fig. 10. (a) Microfabricated piezoresistive cantilever [57]. (b) TSUPREM4 [388] simulation plots of doping profiles using
ion implantation vs. epitaxial deposition techniques. Note the difference in the dopant profiles following ion-implantation and epitaxy
and the progression of dopant diffusion with increasing time of thermal annealing. Courtesy of Sung-Jin Park, Stanford University.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
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ultra thin piezoresistive layers and increased force sen-
sitivity [130]. Harley and Kenny [131] and Liang et al. [132]
demonstrated the use of epitaxially grown doped silicon
to form piezoresistors in ultra-thin cantilevers (less than
100 nm). This is a practical method for such thin piezo-resistive cantilevers, especially given the difficulties of
implanting shallow junction depths (less than 50 nm),
activating dopant atoms, and restoring lattice quality.
Joyce and Baldrey [126] first demonstrated selective
deposition of silicon epitaxial layers using oxide-masking
techniques in 1962 and Zhang et al. [133] demonstrated an
HCl-free selective deposition technique. We have also
demonstrated epitaxial piezoresistors on the sidewalls ofmicrostructures for in-plane sensing applications using
selective deposition techniques [55]. These epitaxial
sidewall piezoresistive sensors showed increased sensitiv-
ity over oblique-angle ion-implanted piezoresistors of the
same dose.
4) Doped Polysilicon: Polycrystalline silicon (polysilicon
or ‘‘poly’’) may be doped by diffusion, ion implantation, orin situ doping. Polysilicon in situ doping introduces gas-
phase dopants with the precursor polysilicon gases during
chemical vapor deposition. However, introduction of dop-
ant gases results in non-uniform polysilicon layer thickness
across the wafer, a lower deposition rate, and dopant non-
uniformity [105]. Moreover, adding dopants during the
deposition of the polysilicon layer also affects layer prop-
erties and changes grain size, grain orientation, and in-trinsic stress. The deposition temperature, anneal time and
anneal temperature determine the surface roughness,
grain size, grain orientation, and intrinsic stress of the
resulting polysilicon layer.
Piezoresistive effects in polysilicon were studied ex-
tensively in the 1970s and 1980s [134]–[146]. French and
Evans presented a theoretical model for piezoresistance in
polysilicon as a function of doping, grain size, and orien-tation and proposed an optimum set of processing param-
eters for a given grain size [145].
5) Tradeoffs in Process Selection: Ion implantation is the
most common method of fabricating piezoresistors. Advan-
tages of ion implantation include precise control of dopant
concentration and depth. Disadvantages include lattice
damage and annealing requirements for dopant activation.Diffusion has the advantage of batch processing, but suffers
from poor dopant depth and concentration control. Epitaxy
provides excellent depth control without annealing, which
enables shallow junctions with abrupt dopant profiles.
However, processing complexity and equipment costs and
availability are drawbacks to epitaxy. Table 1 compares ion-
implantation, diffusion, and epitaxy techniques.
D. Design and Process Effects onPiezoresistor Performance
Design and process parameters affect piezoresistor sen-
sitivity and noise. Sensitivity is a strong function of dopant
concentration and piezoresistor orientation. In choosing the
device geometry, doping, and anneal conditions, the piezo-
resistive device designer must also consider the temperature
coefficients of sensitivity and resistance, nonlinearity withstrain and temperature, and noise and resolution limits.
1) Device Doping and Orientation: Initial experiments by
Smith used bars of silicon cut from wafers doped while
growing the single-crystal ingot [30]. Later, Pfann and
Thurston [35] suggested diffusion techniques to integrate
doped piezoresistors on the sensor surface. The piezoresistive
properties of diffused layers were subsequently investigatedby Tufte and Stelzer [79]. They also provided empirical data
on piezoresistive coefficients for different surface concentra-
tions and resistivities. Kurtz and Gravel replotted their data
and noted that the piezoresistive coefficients decrease
approximately with the log of surface concentration [147].
The early analyses by Smith, and Pfann and Thurston,
covered virtually all crystal orientations and piezoresistor
designs for n-type and p-type piezoresistors in use today.Kanda [47] extended these analyses with graphical rep-
resentations of the piezoresistive coefficients in arbitrary
Table 1 Comparisons of Doping Methods (After Plummer et al. [105])
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
522 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
directions in the commonly used (100) crystal plane and
the less common (110), and (211) planes. These graphs
provide a useful picture of how piezoresistive coefficients
vary with respect to crystal orientations for both longitu-
dinal and transverse geometries (Fig. 11). Kanda also
presented theoretical calculations of piezoresistive changeversus dopant concentration. He suggested a simple power
law dependence of the relaxation time with temperature
and noted a discrepancy between his calculations and the
experimental data for high doping concentrations (Fig. 12).In his notation, the piezoresistive coefficient is calculated
by multiplying the piezoresistive factor, PðN; TÞ (Fig. 13),
by the room temperature piezoresistive coefficient. The
calculated values of the PðN; TÞ, agree well with the
experimental values obtained by Mason [148] for doping
concentrations less than 1� 1017 cm�3, over the temper-
ature range of �50 to 150 �C, but differ by 21% at a
concentration of 3� 1019 cm�3 at room temperature. Theerror was attributed to dopant ions scattering for high
dopant concentrations, whereas the calculation only con-
sidered lattice scattering. Harley [149] later evaluated
data from several researchers and provided an empirical
fit of piezoresistance vs. concentration that better
estimates the sensitivity for higher concentration devices.
Our devices typically fall in a regime described by
extension of Harley’s fit [55]–[57], [150].Four-point bending is used to measure piezoresistive
effects in semiconductors [151], [152], though care must be
taken in high-stress test conditions [104]. Richter et al.[48], [153], [154] demonstrated a novel piezocoefficient-
mapping device to measure 3D stresses in device packaging
and also to extract directional piezoresistive coefficients
(Fig. 14). Using orthogonal h100i piezoresistors and 4-point
bending strain along the h110i direction, they measuredpiezoresistance coefficients for silicon and strained silicon
(Si0:9Ge0:1) molecular beam epitaxial (MBE) grown layers
at boron doping levels of 1� 1018 and 1� 1019 cm�3; they
extracted piezoresistive coefficients as a function of doping
and direction. Their results are higher than Smith’s lower
dose values and also showed that lattice strain raises the
value of �44.
Fig. 11. Room temperature piezoresistive coefficients in the (100)
plane of (a) p-type silicon (b) n-type silicon. These graphics
predict piezoresistive coefficients very well for low doses.
After Kanda [47], � 1982 IEEE.
Fig. 12. Piezoresistive coefficients as a function of doping.
Experimental data obtained by Kerr, Tufte, and Mason are fitted by
Harley and Kenny [79], [148], [149], [157]. Theoretical prediction by
Kanda overestimates the piezoresistive coefficients at higher
concentrations. After Harley and Kenny [149], � 2000 IEEE.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
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2) Temperature Coefficients of Sensitivity and Resistance:Piezoresistors are sensitive to temperature variation, which
changes the mobility and number of carriers, resulting in a
change in conductivity (or resistivity) and piezoresistive
coefficients (sensitivity) [155]. Consequently, doped sili-
con can be used for accurate temperature sensing as inresistance temperature detectors (RTDs). A typical com-
mercial piezoresistive pressure sensor has a thermal resis-
tance change ten times the full-scale stressed resistance
change over a temperature range of 55 �C. Kurtz [156]
presented data and discussed the trend of the piezoresistive
coefficient ð�Þ, temperature coefficient of piezoresistive
coefficient ðTCSÞ, resistivity ð�Þ, temperature coefficient of
resistivity ðTCRÞ and strain nonlinearity, as a function ofdopant concentration (Fig. 15).
Kurtz was the first to clearly highlight the advantages of
using higher doping levels for piezoresistors. The temper-
ature dependence of sensitivity decreases with increasing
surface concentration. This trend is desirable except that
increasing surface concentration also sacrifices the sensi-
tivity of the piezoresistors. However, the temperature
coefficient of sensitivity drops off faster than sensitivity.Also at higher doping levels, the strain and temperature
nonlinearities in sensitivity, and temperature change ofresistance are very much reduced. Some piezoresistive
pressure sensor manufacturers, such as Kulite Semicon-
ductor Products, Merit Sensors, and GE NovaSensor
manufacture high-dose piezoresistors, taking advantage
of this reduced temperature sensitivity. Ultimately some
temperature dependence in silicon strain sensors is
inevitable though this dependence may be compensated
by the use of a half or full-active Wheatstone bridge andconditioning circuitry (Section III-E).
Tufte and Stelzer [79] first presented detailed measure-
ments of these parameters for diffused layers over a wide
range of dopant concentrations ð1018 � 1021 atoms cm�3Þand temperatures (�90 �C to 100 �C). They also showed
that the piezoresistive coefficient was relatively insensitive
to the diffusion depth for a diffused layer. Kerr and
Milnes [157] showed that the surface dopant concentrationcould be used as an adequate proxy for the average effective
concentration in modeling the piezoresistivity of diffused
layers. More recently, refined concentration-dependent
temperature sensitivity measurements have been reported
on integrated die using 4-point bending and finite element
analysis of stress profiles [158].
3) Nonlinearity: The response of piezoresistors to stressis nonlinear at larger strain (9 0.1%). Understanding and
Fig. 14. (a) Stress sensor chip with a p-type circular piezoresistors in
the middle of the chip. (b) Schematic diagram of the circular
piezoresistor with a radius of 1700 �m. From Richter et al. [154],
� 2007 IEEE.
Fig. 13. The adjusted piezoresistance factor P(N,T) as a function of
impurity concentration and temperature for (a) p-type silicon
(b) n-type silicon. These graphics predict piezoresistive coefficients
very well for low doses but the trends with temperature are correct.
After Kanda [47], � 1982 IEEE.
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524 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
compensating for the nonlinearity of piezoresistors is im-
portant for precision piezoresistive devices. Matsuda et al.[159], [160] calculated and measured the piezoresistive
coefficients and third-order effects for both p-type andn-type silicon for the three major crystallographic orienta-
tions with strain up to 0.1%. Higher strain levels were
difficult to measure since surface defects in the silicon
lattice cause fracture at low strain levels. Addressing this
problem, Chen and MacDonald [161] co-fabricated a
microactuator and a 150-�m-long, 150-nm-diameter single-
crystal silicon fiber from one single-crystal silicon substrate
to reduce the possibility of defects, allowing measurements
of strains greater than 1%. With the increased range ofstrain, the second and third order fit for piezoresistive
coefficients were quantified more accurately (Fig. 16).
Table 2 shows the results obtained by Chen and MacDonald
compared to the data obtained by Tufte and Stelzer [162].
Additional studies of the effects of strain on semiconductor
properties have been undertaken recently as interest in
strained substrates has increased [48], [73], [104], [163].
Fig. 15. Trends of key piezoresistive properties with concentrations,
such as (a) longitudinal piezoresistive coefficient (sensitivity)
(b) temperature coefficient of sensitivity (c) temperature coefficient of
resistivity with dopant concentration. After Kurtz and Gravel [147].
� 1967 Industrial Automation Standards.
Fig. 16. (a) SEM image of micro-actuator and 150-�m-long,
150-nm-diameter, phosphorous-doped, h110i silicon fiber
(test sample) with resistivity of 0.6 m� cm. (b) Percentage change
longitudinal piezoresistance vs. strain exhibited less nonlinearity at
low strain than previous reports at lower doping (Data of
Matsuda et al. [161] were included by converting stress data using
Young’s modulus of 170 GPa). Reprinted with permission from
Chen and MacDonald [161], � 2004 American Institute of Physics.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 525
E. Noise in PiezoresistorsElectrical noise is the random variation in the potential of
a conductor. The electrical noise in a piezoresistor sets the
fundamental lower limit of piezoresistive transducer resolu-
tion. The dominant random electrical noise sources in piezo-
resistors are Johnson (thermal) noise and 1=f (flicker) noise.
Other noise sources, such as inductive or capacitive line
pickup also exist [51]. Also, for many applications the accu-
racy of piezoresistive transducers is limited by temperature
effects or thermo-mechanical hysteresis, e.g., in commercialpiezoresistive devices such as piezoresistive pressure sensors.
Integrated shield layers have been shown to reduce noise
effects, including temperature sensitivity [164].
1) Thermal Noise: Thermal noise, also known as Johnson
or Johnson-Nyquist noise, is universal to resistors. It was
first observed in 1928 by Johnson [164] and theoretically
explained by Nyquist [165]. Thermal noise is a function ofthe absolute temperature TðKÞ of the resistor, resistance
value Rð�Þ, and Boltzmann’s constant k (J/K). For a 1 Hz
bandwidth the thermal noise is:
Vj ¼ffiffiffiffiffiffiffiffiffiffi4kTRp
: (11)
Thermal noise is fundamental, exists in all resistors,and cannot be eliminated. A discussion on thermal noise in
modern devices can be found elsewhere [166].
2) 1=f Noise: The power spectral density of 1=f noise, as
its name implies, is inversely proportional to frequency.
The origins of 1=f noise are still not fully understood and
remain an active topic of research [167]–[178]. In partic-
ular, 1=f noise in piezoresistors is dependent on fab-rication process parameters, such as implant dose and
energy, and anneal parameters. A 1=f n noise exponent of
n 9 1 can be a measure of conductor reliability. Excessive
1=f noise can indicate poor fabrication process quality
[179], [180]. Several researchers have presented piezo-
resistive device optimization to include 1=f noise [149],
[181]–[183].
Despite many decades of research, the source of 1=fnoise is still debated [176]. McWhorter and Hooge
proposed two opposing theories of 1=f noise. These views
are currently the leading explanations for the origin of 1=f
noise. The McWhorter model attributes the 1=f noise to
surface factors [184], [185], while the Hooge modelimplicates bulk defects [167], [177] (Fig. 17).
Experiments show that 1=f noise is due to conductivity
fluctuations in the resistor [177], [178]. Hooge showed that
the 1=f low-frequency noise modulated the thermal noise
even with no current flowing through the resistor [172]. This
experiment demonstrates that 1=f noise is not current-
generated. Current is only needed to transform the conduc-
tivity fluctuations into voltage fluctuations. Thermal and 1=fnoise are fundamentally different. Thermal noise is a voltage
noise; therefore it does not depend on the amount of current
in the resistor. In contrast, 1=f noise is a conductivity noise;
therefore the voltage noise is proportional to the current in
the resistor.
Table 2 Piezoresistive Coefficients Using Data From 0% to 1% Strain. From Chen and MacDonald [161], Reprinted With Permission From American
Institute of Physics
Fig. 17. Conductivity fluctuations based on (a) Hooge model
(bulk effect) (b) McWhorter model (surface effect). Courtesy of
Paul Lim, Stanford University.
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526 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
Hooge’s empirical 1=f noise model, fit to observed data,predicts that the voltage noise density is given by:
V1=f ¼ Vb
ffiffiffiffiffi
Nf
r(12)
where f , N, and Vb, are frequency, total number of carriersin the resistor volume, and bias voltage across the resistor,
respectively. A non-dimensional fitting parameter, , is
ascribed to the ‘‘quality of the lattice’’ and typically ranges
from 10�3 down to 10�7 [56], [149], [183].
Attempts to observe the lower limit of 1=f , below
which the spectrum theoretically flattens, have not been
successful [177]. Measurements down to 3 �Hz (or
approximately 4 days per cycle) show a noise spectrumthat is still 1=f [186]. Harley and Kenny showed that
resistors with different surface to volume ratios have the
same 1=f noise characteristics, and 1=f noise scales with
the resistor volume, consistent with Hooge’s empirical
equation [149].
Hooge defines 1=f noise as only those spectra with a
frequency exponent of 0.9–1.1. Noise with a different
power spectral density and other frequency exponents,sometimes referred to as 1=f -like noise, is often confused
with 1=f noise and is not predicted by the Hooge equation.
According to Hooge, noise with a higher exponent, e.g., 1.5
or 2, indicates noise mechanisms other than mobility
fluctuations that should not be considered 1=f noise and
are not predicted by (12). Abnormal 1=f noise character-
ization can give insights into piezoresistor reliability and
failure analyses. For example, Neri [187] found that the 1=fexponent is closer to 2 in metal traces that exhibit
electromigration. Vandamme [188] showed that excess 1=fnoise in semiconductors can be attributed to small
constrictions and current crowding. Devices with con-
striction resistance show third harmonics and nonlinea-
rities in their output.
Current crowding theory also explains why polysilicon
has higher 1=f noise than its crystalline counterpart [168].At grain boundaries, small constrictions are present, thus
reducing the total number of carriers ðNÞ and effectively
increasing the 1=f noise. Basically, 1=f voltage noise does
increase linearly with the applied excitation. If the noise
spectrum trends otherwise, then other mechanisms, such
as current crowding, could be present. The noise floor of
the experimental setup may be verified by reducing the
applied excitation and observing only the thermal noise ofthe piezoresistor.
Reducing 1=f noise is important for low frequency
applications. Chemical and bio-sensing applications based
on displacement transduction require static and low
frequency measurements and require stability over time
periods of tens of seconds to many hours. Lower 1=f -noise
piezoresistors are required for these applications. The
fabrication process parameters can be tailored to achievelow 1=f noise amplitude spectral densities. As suggested by
Kanda’s model, low impurity doping is often used to
achieve high sensitivity. However, this model under-
estimates sensitivity at high and low doping and leads to a
device design that poorly trades-off sensitivity with noise
for lower frequency applications. The empirical data of
Tufte and Seltzer [79], on the other hand, offer better
guidance in these regimes. The advantages of high dopingare lower noise and lower temperature coefficients for
modest reduction of sensitivity. For example, if peak
doping concentration, Cpeak, decreases from 1019 cm�3 to
1017 cm�3, the sensitivity increases by only 65% while the
noise increases by a factor of ten. From (12), the 1=f noise
can be reduced by increasing N, the total number of
carriers dependent on piezoresistor volume and impurity
implant dose, and reducing . Vandamme [179], [189]showed that depends on crystal lattice perfection and
lattice quality increases with higher temperature anneals
and longer anneal times. Mallon et al. [56] extended the
work of Harley and Kenny [56], [149] and showed that
long, high temperature anneals can produce lower noise
piezoresistors with low values of (Fig. 18).
Fig. 19 shows the typical 1=f noise of a piezoresistor.
The horizontal straight line is the thermal noise of theresistor. For reference, a 1 k� resistor has 4 nV=
pHz
thermal noise; other resistor values are easily referenced to
this value. The thermal noise of a resistor is also an excellent
source to calibrate and verify the measurement system [190].
The straight, sloped line is the 1=f noise of the resistor,
which depends on the applied bias voltage. If the resistor is
unbiased, the 1=f noise disappears, while the thermal noise
remains. The 1=f noise is proportional to applied biasvoltage with proportionality constant
ffiffiffiffiffiffiffiffiffiffiffi=Nf
p. The total
Fig. 18. Hooge noise parameter, , improves (decreases) with
increasing anneal diffusion length,pDt. Reprinted with permission
from Mallon et al. [56]. � 2008 American Institute of Physics.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 527
noise is the sum of thermal and 1=f noise. Since the noise
sources are uncorrelated they are additive as,
VTotalNoise ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2
thermal þ V21=f
q: (13)
III . DEVICES AND APPLICATIONS
Piezoresistors are widely used in pressure, force and
inertial sensors. An external force creates a deflection or
stretch in the structure proportional to the measurand, and
piezoresistance varies proportional to the applied stress.
When used in a Wheatstone bridge or other conditioning
circuit, the change in resistance is converted to change involtage output. In this section, we review some of the most
commonly used devices that employ piezoresistive trans-
duction schemes in microsystems as well as common
signal conditioning approaches. For brevity we focus on
seminal and representative examples of the art.
A. Cantilever SensorsCantilevers are beams with one free and one fixed end
(Fig. 20). A piezoresistive cantilever force sensor normally
has a piezoresistor at the root of the beam, near the top
surface to maximize sensitivity. From beam mechanics, themaximum stress ð�Þ occurs at the outer surface of the root
(y ¼ �h=2, x ¼ 0), when an external force ðFÞ is applied
at the end of a cantilever ðx ¼ LÞ:
� ¼ 12Fðx� LÞybh3
(14)
where x is the distance along the length of the cantilevermeasured from the root, y is the distance along the
thickness of the cantilever measured from the neutral axis,
b is the width, and h is the thickness of the cantilever.
The change in resistance is a function of the stress in the
piezoresistor. The cantilever is a ubiquitous structure in the
field of micromachined transducers. Cantilevers are
relatively simple and inexpensive to fabricate, and analyt-
ical solutions of displacement profiles and stress distribu-tions under load are well developed [49]. Cantilever beams
are commonly used as force and displacement sensors as
well as mass sensors when excited in resonance. Various
schemes can transduce the force applied to the cantilever
by measuring the stress (piezoresistive) or displacement
(optical, capacitive) at any location on the cantilever.
The earliest work on integrated silicon piezoresistive
cantilevers started in the late 1960s, when Wilfinger [191]used a silicon cantilever with diffused piezoresistive elements
as a Fresonistor_ (resonator). The silicon cantilever was
mechanically deflected by electrically induced thermal expan-
sion. The piezoresistors were used to detect the maximum
stress at the resonant frequency. Fulkerson [192] integrated a
bridge and an amplifier circuit in a microfabricated piezo-
resistive cantilever sensor to linearize and amplify the output,
pioneering the concept of signal conditioning integration.Numerous resonant, piezoresistive cantilever devices have
been implemented for mass sensing, chemical sensing, and
inertial sensing since that time [193]–[195].
Perhaps the best-known application of cantilevers as force
and displacement sensors is in Atomic Force Microscopy
(AFM). AFM was invented by Binnig, Quate, and Gerber in
1986 as the first tool capable of investigating the surface of
both conductors and insulators at the atomic scale [196]. Thefirst AFM combined Scanning Tunneling Microscopy (STM)
technology [197] and a stylus profilometer. This AFM used
tunneling current for cantilever displacement detection and
achieved lateral and vertical resolutions of 30 A and less than
1 A, respectively. Since then, other detection methods such as
optical [198] and capacitive [199], [200], have been used to
detect the displacement of the AFM cantilever. However,
these methods require a sensing element external to thecantilever. In 1993, Tortonese et al. first used piezoresistive
transduction to detect AFM cantilever displacement [130].
Fig. 19. Typical noise curve of a full-bridged piezoresistor.
The sloped solid line is the total noise dominated by 1=f-noise
component, while the horizontal solid line is the total noise dominated
by thermal-noise component. The 1=f noise corner frequency is the
frequency at which the thermal noise is equal to the 1=f noise. In this
noise spectrum, the corner frequency is �1 Hz. The horizontal dashed
line is the measurement system noise level, which is verified with a
680 � resistor from 0.01 Hz. For clarity, system noise is not shown
above 1 Hz. The noise is measured using modulation-demodulation
technique (Section III-E). The roll-off above 60 Hz is due to system
bandwidth. Reprinted with permission from Mallon et al. [56].
� 2008 American Institute of Physics.
Fig. 20. A cantilever with applied force at the tip and the resulting
stress profile in the beam. The maximum stress occurs at outer surface
of the root (y ¼ �h=2, x ¼ 0).
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
528 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
The scheme achieved 0.1 Arms vertical resolution in a
10 Hz–1 kHz bandwidth. Piezoresistive transduction is
attractive in its simplicity and reliability because: 1) theabsence of external sensing elements simplifies the design of
an AFM for large samples and adverse environments (high
vacuum, etc.) and reduces the cost of the experimental
setup; 2) the operation of the microscope is further simplified
by eliminating the need for precise system alignment;
3) piezoresistive AFM requires low voltages and simple
circuitry for operation.
Several innovations increased the visibility of piezo-resistive AFM for specialized applications. AFM piezoresistive
cantilevers have been improved for parallel high-speed imag-
ing. Integrated actuators (thermal or piezoelectric) allowed
increased bandwidth (0.6–6 kHz) by bending the cantilever
over sample topography rather than moving the sample up
and down with a piezotube [201], [202]. Brugger et al.demonstrated lateral force measurements using surface
piezoresistors on AFM cantilevers [203]. Chui et al. [122]later introduced sidewall-implant fabrication for dual-axis
piezoresistive AFM cantilever applications. The dual-axis
AFM cantilevers utilize regions with orthogonal compliance
to reduce mechanical crosstalk when an AFM cantilever is
operated in a torsional bending mode and allow improved
measurement of lateral forces at the tip (Fig. 21). Brugger et al.also fabricated and tested ultra-sensitive piezoresistive
cantilevers for torque magnetometry [204]. Hagleitner et al.fabricated the first parallel scanning, piezoresistive AFM
cantilevers integrated with on-chip circuitry using Comple-
metary Metal Oxide Semiconductor (CMOS) technology
[205]. A review of advances in piezoresistive cantilevers for
AFM until 1997 is available elsewhere [206].
Piezoresistive cantilevers have also been widely usedfor environmental [207], chemical [208], [209], and bio-
logical [210]–[218] sensors. Boisen et al. developed AFM
probes with integrated piezoresistive read-out for envi-
ronmental sensing [207]. The sensors had a resolution
less than 1 A and facilitated measurement in both gaseous
and liquid environments. Franks et al. fabricated piezo-
resistive CMOS-based AFM cantilevers for nanochemical
surface analysis application [219]. Baselt et al. reviewedmicromachined biosensors and demonstrated the use of
piezoresistive AFM cantilevers for the study of interac-
tions between biomolecules and chemical sensors [210].
Fig. 21. (a) Dual-axis AFM cantilever with orthogonal axes of compliance. Oblique ion implants are used to form electrical elements
on vertical sidewalls and horizontal surfaces simultaneously. (b) SEM Image of a dual-axis AFM cantilever. Reprinted with
permission from Chui et al. [122]. � 1998 American Institute of Physics.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 529
Piezoresistive cantilevers have also been used formaterials characterization [220]–[222], liquid or gas
flow velocity sensing [223], [224] and data storage
applications [225]–[227]. However, researchers have
found that thermal-based cantilevers perform better
(more than one order of magnitude) in terms of sensitivity
and resolution for data storage applications compared to
the piezoresistive cantilevers [228]–[230]. Aeschimann et al.developed piezoresistive scanning-probe arrays for opera-tion in liquids [231]. Their cantilevers were passivated
with 50-nm silicon nitride films over the piezoresistors
and 500-nm silicon oxide films over the metal lines. They
also fabricated ‘‘truss’’ cantilevers to reduce the hydrody-
namic resistance or damping in liquids.
Researchers have also pushed the limits of micro-
fabrication to make ultra thin cantilevers. Harley and
Kenny fabricated 890 A thick single crystal siliconcantilevers using epitaxial deposition with sensitivity of
5:6� 10�15 N=ðHzÞ1=2 in air [131]. Liang et al. showed
700 A thick n-type piezoresistive cantilevers with sensi-
tivity of 1:6� 10�15 N=ðHzÞ1=2 at 1 kHz [132]. Harley and
Kenny and Liang et al. formed the piezoresistors by
growing doped epitaxial layers, which allowed the
fabrication of ultra thin piezoresistors and cantilevers.
However, Bergaud et al. showed that ion-implantationtechnique could also be used to fabricate ultra-thin piezo-
resistors (900 A) by implanting Boron Fluorine (BF2) into
germanium-prearmorphized silicon [232]. They found that
the experimental sensitivity was 80% of their theoretical
prediction and that the germanium prearmorphization
step did not affect the sensitivity of the piezoresistors.
Bargatin et al. developed a novel method to detect dis-
placement and resonance up to 71 MHz using piezo-resistors as signal downmixers [233]. They tested their
scheme using nanoscale silicon and AlGaAs piezoresistive
cantilevers (1100-A thick) and demonstrated that the
downmixed signal is approximately 1000 times larger
than in the standard scheme (using high-frequency net-
work analyzer). The same group later reported nanoscale
silicon carbide (SiC) cantilevers with piezoresistive gold
films for very high-frequency (VHF) applications inScanning Probe Microscopy (SPM) [234]. Their smallest
cantilever, 0:6 �m� 0:4 �m� 700 A, with a first reso-
nant frequency of 127 MHz and 1=f noise corner frequency
of 100 Hz, was sensitive to thermomechanical self-noise.
These devices fall into the category of piezoresistive Nano-
Electro-Mechanical Systems (NEMS) and reviews on
NEMS are available elsewhere [218], [235], [236].
Harley and Kenny reported optimization of thin (epi-taxial), power-limited piezoresistive cantilevers for AFM
applications [149]. The methods and analyses are extensible
to other types of piezoresistive sensors. Three design aspects
were discussed: geometric (thickness, length, and width),
processing (dopant depth, dopant concentration, and sur-
face treatment and anneal), and operation (bias voltage).
Park et al. [57] extended this optimization to the general
case of ion-implanted piezo resistors. Sensitivity in a singlepiezoresistor, ion implanted cantilever may be expressed as
SF� ¼�RR
F¼
12 l� 12
lp� �
�l max
bt3
Rt=2
�t=2
q�pPzdz
Rt=2
�t=2
q�pdz
; (15)
where SF is the force sensitivity (V/N), �l max is the maximum
longitudinal piezoresistive coefficient (Pa�1), l is the length of
the cantilever (m), lp is the length of the piezoresistor (m), b isthe width of the cantilever (m), t is the thickness of the
cantilever (m), p is the doping density (cm�3), � is the dopant
mobility (cm2 V�1 s�1), q is the electronic charge, P is the
piezoresistance factor, z is the distance to the neutral axis of
the cantilever and �� is the efficiency factor,
�� ¼ 2
t
Rt=2
�t=2
q�pPzdz
Rt=2
�t=2
q�pdz
: (16)
The efficiency factor, ��, accounts for an arbitrary doping
profile, e.g., ion-implanted, convolved with the stress profile
and competing effects of dopant diffusion on sensitivity.
Yu et al. performed a similar analysis for piezoresistivecantilevers used in micro-channels [183]. Yu et al. also
compared types of piezoresistive material (amorphous,
microcrystalline, and single-crystal silicon) in their analysis.
Yang et al. reported design and optimization of piezoresistive
cantilevers for biosensing applications using finite element
analysis, and analyzed the change in relative resistivity in the
presence of a chemical reaction [213]. Optimization of
piezoresistive cantilevers for chemical sensing has also beenshown to differ significantly from optimization for force or
displacement probing [389], [390]. Hansen and Boisen
provided design criteria for piezoresistive AFM cantilevers
by investigating the devices’ noise performance [181]. They
took into account vibrational noise of the cantilever, Johnson
and 1=f noise of the piezoresistor, and the effect of self-
heating from the input power on the total noise.
B. Strain GaugesThe measurement of strain is important in numerous
applications in science and engineering and metallic strain
gauges are widely used. The measurement principle is based
on the change in electrical conductance and geometry of a
stretched conductor, as described in Sections II-A3 and II-B.
Higson reviewed advances in mechanical bonded resistance
strain gauges, from their introduction in 1938 to 1964 [237].
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
530 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
The discovery of the piezoresistive effect in silicon andgermanium by Smith in 1954 [30] generated significant
interest in semiconductor strain sensing. Kulite Semicon-
ductor and Microsystems developed commercial products in
the late 1950s [33]. These first-generation semiconductor
strain gauges were used for making stress measurements.
The gauges were organically bonded to metal flexural
elements to make pressure sensors, load cells and accel-
erometers (Fig. 2). More recently stress sensitive rosettepatterns have been integrated onto silicon die to measure
integrated circuit packaging stresses [238] Creatively,
Schwizer et al. used piezoresistive rosettes to measure wire
bonding forces and flip chip solder ball process parameters
[239], [240]. Planar arrangements of pseudo-hall effect
strain sensors have also been demonstrated for 3D sensing
when coupled with an input arm such as a joystick or
coordinate measuring probes [59], [391].
C. Pressure SensorsPiezoresistive pressure sensors are some of the
most reported and developed micromachined devices.
Esashi et al. [241] reviewed micromachined pressure sensors
with various transduction mechanisms and principles. In
this paper, we focus on piezoresistive pressure sensors,
which typically measure deflection (deformation) of a thincircular or rectangular membrane (diaphragm) under an
applied external pressure (Fig. 22). The membrane may be
made from the same material as the wafer substrate (silicon,
diamond, etc.) or CVD-based thin films (oxide, nitride, etc.).
Integrated piezoresistors are formed by dopant diffusion, ion
implantation, or doped epitaxy. Maximum stress occurs at
the edge of the membrane so piezoresistors are usually
located near the edge to maximize sensitivity.Kulite-Bytrex and Microsystems introduced commercial
metal-diaphragm pressure sensors in the late 1950s [33].
Semiconductor-based strain gauges were epoxy-bonded to
the surface of a machined metal diaphragm. Typically, four
semiconductor strain gauges were employed, two in tension
at the diaphragm center and two at the edge, allowing
configuration into a four active arm Wheatsone bridge
which: provided a voltage output proportional to �R=R,increased sensitivity, nulled the output, and provided a first
order correction for zero shift with temperature. These
sensors were intended for high-cost, low-volume industrial,
aerospace, and biomedical applications. These miniature
devices had relatively low performance by today’s standards.
They suffered especially from poor zero stability due to the
mismatch between the thermal expansion coefficients of
the silicon strain gauge and the stainless steel diaphragmand the relatively poor stress transmission characteristics of
the metal-epoxy-silicon interface, which caused creep and
hysteresis. In 1959, Burns patented one of the earliest
diaphragm-based piezoresistive semiconductor micro-
phones [242]. Although intended as acoustic transducers,
the operation principles were similar to those of piezo-
resistive pressure sensors.
In 1962, Tufte et al. [36] reported the first siliconpressure sensors with piezoresistors integrated with the
diaphragm using dopant diffusion. These diffused piezo-
resistive pressure sensors eliminated the epoxy bonding
and replaced the metal diaphragm with single-crystal
silicon, improving the performance of the sensors signif-
icantly. Following this, Peake et al. [243] developed an
integrated circuit digital, diffused silicon, piezoresistive
pressure sensor for air data applications in 1969.
Fig. 22. Illustration of a piezoresistive pressure sensor. (a) Top view of
piezoresistive pressure sensor. Four piezoresistors are placed on each
edge forming a Wheatstone bridge circuit. (b) Cross section A-A
showing deflected diaphragm with piezoresistors at maximum stress
locations. (c) Photograph of a pressure sensors with four 3C-SiC
(a polytype of silicon carbide, see Section IV-A) piezoresistors.
From Wu et al. [336]. � 2000 IEEE.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 531
In the late 1960s and early 1970s, three microfabricationtechniques, anisotropic chemical etching of silicon, ion
implantation, and anodic bonding, were developed. These
techniques played a major role in improving the perfor-
mance of microfabricated pressure sensors. Anisotropic
etching and anodic bonding allowed batch fabrication of
pressure sensors, reducing the cost of the production. In
addition, these technologies enabled miniaturization, in-
creased sensitivity, and precise placement and dose of thepiezoresistors. In 1967, Stedman [244] pioneered bossed-
diaphragm pressure sensors. Samaun et al. [245] used
anisotropic etching to form the silicon diaphragm and
showed a significant increase in sensitivity of the sensor.
Wilner [246], [247] further improved sensitivity and
linearity by placing piezoresistors in the transverse direction
at the concentrated stress locations and introduced sculp-
tured diaphragms. In 1977, Marshall [248] at Honeywellpatented the first silicon-based pressure sensor using ion
implantation. In 1978, Kurtz et al. [249] at Kulite Semi-
conductor invented a low pressure, bossed-diaphragm,
pressure transducer with good sensitivity and linearity at
low pressure. In the 1970s, Kulite Semiconductor and
Honeywell, Inc. began to produce and make widely available
commercial integrated pressure sensors. Clark and Wise
enabled refined designs with derivation of the governingelectromechanical equations of thin diaphragm silicon
pressure sensors using finite difference methods [250].
The solutions were presented in dimensionless form
applicable to anisotropically etched square diaphragms of
arbitrary size and thickness.
From the 1980s to the present, continued improve-
ments in fabrication technologies, such as anisotropic
etching, photolithography, dopant diffusion, ion implan-tation, wafer bonding, and thin film deposition, have
allowed further reduction in size, increase in sensitivity,
higher yield, and better performance (Fig. 23). Several
microfabrication techniques have been developed and
employed to precisely control diaphragm thickness.
Jackson et al. and Kim and Wise used an electrochemicalP-N junction as an etch stop, taking advantage of
significantly different etch rates of p-type and n-type
silicon (3000:1 in ethylene diamine-based etchants) [251],
[252]. Kloeck et al. [253] reported improved output
characteristics of piezoresistive pressure sensors fabricated
with electrochemical etch-stop techniques. In the late
1980’s Novasensor introduced the use of silicon fusion
bonding to MEMS sensors [254]. NovaSensor used thistechnique combined with controlled thinning techniques,
such as boron etch stopped etching and p-n electrochemical
etching, to produce a number of piezoresistive sensors.
These sensors included low-pressure sensors with sculp-
tured bosses, high-pressure and high-temperature sensors,
sensors with precision stop overload protection, and
accelerometers [255]–[258].
Chau and Wise [259] provided scaling limits for ultra-miniature and ultra-sensitive silicon pressure sensors based
on Brownian noise, electrical noise, electrostatic pressure
variations, and pressure offset errors due to resistance
mismatch. Spencer et al. [260] compared noise limits for
piezoresistive and capacitive pressure sensors integrated with
typical signal conditioning for varying diaphragm thickness,
diameter, and gap. Regardless of the sensor dimension,
piezoresistive sensors configured in a Wheatstone bridgeachieved the best resolution. Sun et al. [261] presented a
theoretical model of the reverse current (leakage current
across the piezoresistor-substrate p-n junction) and its effect
on thermal drift of the bridge offset voltage. They found
cleaner processing, gettering of metal impurities, and
contamination control reduced the reverse current and
offset errors.
Bae et al. [262] reported a design optimization of apiezoresistive pressure sensor considering the piezo-
resistor lengths and number of turns and showed that
the optimal design is significantly different when noise in
considered. The optimal output signal-to-noise ratio was
2.5 times that of the sensor designed maximizing the
Fig. 23. The evolution of micromachined pressure sensors from 1950s to 1980s. After Eaton and Smith [102].
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
532 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
output voltage alone. Kanda and Yasukawa consideredseveral factors in their optimization of piezoresistive
pressure sensors including: the shape of the diaphragm
(square or circular); the thickness uniformity of the
diaphragm (with or without a center boss); anisotropy of
the piezoresistivity and elasticity; and large deflection of
diaphragms [46]. They introduced a new index, �(modified signal-to-noise ratio), which allowed them to
optimize the crystal planes of the diaphragm and thecrystal directions of the piezoresistors, regardless of the
dimensions. They found that a square diaphragm with a
center boss on a (100) plane with four piezoresistors
aligned along the h111i direction was the optimum
design. Bharwadj et al. reported on signal-to-noise ratio
optimization of piezoresistive microphones and took into
account the placement of piezoresistors, geometry,
process condition, and bias voltage [182]. These micro-phones are based on a pressure-sensitive diaphragm,
similar to that of pressure sensors.
The design, manufacture and processing of silicon
piezoresistive pressure sensors has achieved a high level of
sophistication. An example is the Bosch piezoresistive
pressure sensor shown in Fig. 24. This sensor is used to
measure atmospheric and manifold pressure in electronic
engine control systems. Researchers at Bosch developed anew technique for these piezoresistive pressure sensors
using porous silicon and epitaxy to form a single crystal
silicon membrane and vacuum cavity without bonding
[263], [264]. This approach saves wafer real estate and is
CMOS compatible.
Most pressure sensors manufactured today still use
piezoresistive transduction. Advantages of piezoresistive
sensing compared to capacitive sensing include ease ofdifferential pressure sensing configurations and freedom
from the film stress related errors and failures of surface
micromachining.
D. Inertial Sensors
1) Accelerometers: Accelerometers are another heavily
commercialized MEMS application. A comprehensivereview of micromachined inertial sensors, including piezo-
resistive accelerometers, was provided by Yazdi et al. [265],
Accelerometers are widely used in automotive (crash
detection and stability control), biomedical (activity mon-
itoring), consumer electronics (portable computing, cam-
eras lens stabilization, cellular phones), robotics (control
and stability), structural health monitoring, and military
applications. Gyroscopes can be used together withaccelerometers to provide additional information on angu-
lar velocity for navigation purposes in automotive, robotics,
and military applications.
A mechanical accelerometer consists of a proof mass, m,
sprung from beams (spring constant, k), anchored to a fixed
substrate (Fig. 25). The proof mass motion is damped by
viscous effects (damping constant, b) of any surrounding
fluid. The resonant frequency ð!oÞ and the quality factor
ðQÞ of the system can be calculated from
Q ¼ m!o
b(17)
where;
!o ¼ffiffiffiffik
m
r: (18)
In the late 1960s, Gravel and Brosh [266] reported on adiffused, chemically micromachined, integrated silicon
beam accelerometer. Roylance and Angell introduced
the first fully integrated piezoresistive micromachined
Fig. 24. Bosch porous silicon pressure sensor. (a) Sensing diaphragm
and cavity cross section. (b) Pressure sensor with mixed signal
integrated CMOS signal conditioning electronics. (c) Ceramic surface
mount packaged sensor. � Bosch. Pictures: Bosch.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 533
accelerometers in 1978 for biomedical applications [267],
[268]. The accelerometer consisted of a piezoresistive
cantilever with an integrated micromachined lumped mass
at the end and a diffused piezoresistor at the root of the
flexure. The device layer was fully packaged inside a pair of
pyrex glass wafers. The glass wafers served to protect the
device from the environment and to limit proof mass travel.Barth et al. [269] introduced the first commercialized
piezoresistive accelerometer using silicon fusion bonding to
provide an integral package and over pressure stop.
Monolithic integration of piezoresistive accelerometers
with CMOS circuitry subsequently improved the output
readout and accommodated temperature compensation
circuitry [270], [271]. Allen demonstrated piezoresistive
accelerometers with self-test features [272]. Chen et al.integrated a novel vertical beam structure in a piezoresistive
accelerometer to allow in-plane and out-of-plane accelera-
tion measurements [273]. Kwon and Park [274] fabricated a
three axis piezoresistive accelerometer using bulk micro-
machining and silicon direct bonding technology using a
polysilicon layer. Partridge et al. [123] and Park et al. [124]
used oblique ion-implantation for the piezoresistors with
DRIE to fabricate devices designed for lateral accelerationsensing. These devices also incorporated a novel wafer-level
packaging technique using a thick polysilicon epitaxial cap
to seal the devices and protect the piezoresistors from harsh
plasma processing. This protection reduced the noise and
package footprint [275]. Park et al. also reported using a
fully packaged sub-mm scale piezoresistive accelerometer,
for vibration measurements in middle ear ossicles (Fig. 26).
This technology could provide an alternative sensingmethod for implantable hearing aids [276]. Lynch et al.integrated piezoresistive planar accelerometers with wire-
less sensing unit for structural monitoring [277].
Today, piezoresistive transduction vies with capacitivetransduction as the most popular sensing mechanism for
commercial accelerometers. Many Japanese accelerometer
manufacturers (e.g., Hitachi Metals, Matsush*ta, Fujitsu,
and Hokuriku) use piezoresistive transduction, while man-
ufacturers from the US and Europe (e.g., Bosch, Freescale,
Kionix, STMicroelectronics and Analog Devices) focus
mainly on capacitive sensing. Other companies, such as
SensoNor (now Infineon) and Novasensor (now GE sensing)have also demonstrated piezoresistive accelerometers in
production. Both sensing mechanisms utilize CMOS inte-
grated circuits for amplification and compensation, either a
monolithic (Analog Devices) or hybrid approach. Large
manufacturers of automotive sensors prefer capacitive
sensing with integrated self-test by electrostatic actuation.
Three-axis sensing capability, size, and cost are becoming
important factors as demand for consumer electronics withaccelerometer sensing increases, especially in portable
devices and game consoles.
Fig. 25. An accelerometer is modeled as a second order system with a
proof mass (m), spring (k), and damper (b). The displacement (x) is
proportional to the acceleration (A) in the x-direction. The range of the
proof mass movement is limited by the end stops, which protect the
device from shock damage.
Fig. 26. (a) Oblique-view SEM of a sidewall-implanted (41� from the
vertical axis) piezoresistive accelerometer with a 20-�m-thick epi-poly
encapsulation. (b) Optical photograph of the completely packaged
piezoresistive accelerometer with flexible circuit wiring. The sensor is
shown in the background of table salt crystals. From Park et al. [276].
� 2007 IEEE.
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
534 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
2) Gyroscopes: Inertial gyroscopes measure rate ofrotation and operate by detecting inertial resistance to
changes in velocity, e.g., by detecting precession forces
when tilting a spinning mass or via Coriolis forces on a
vibrating mass. Most micromachined gyroscopes are based
on vibration and use the transfer of energy between two
orthogonal vibration modes via the Coriolis force. The
Coriolis force, Fc, induces acceleration (in y) of the mass
proportional to vibration velocity (in x) and angular rate ofrotation (about z): Fc ¼ 2 m�Xip!r cosð!rtÞ, where m is
mass of the proof mass, is magnitude of a rotation
vector, and Xip!r cosð!rtÞ is the in-plane velocity of the
proof mass (Fig. 27). Micromachined gyroscopes are
difficult to manufacture because they require a high
performance resonator and an accelerometer coupled in a
high-vacuum hermetic package. Few MEMS gyroscopes
utilize piezoresistive detection but these require anothertransduction method for the vibration, e.g., Paoletti et al.and Voss et al. demonstrated piezoresistive sensing in a
tuning-fork gyroscope driven by piezoelectric and electro-
magnetic forces, respectively (Fig. 28) [278], [279].
Gretillat et al. improved this design by creating a higher
symmetry mechanical structure using Advanced Deep
Reactive Ion Etching (ADRIE) and separating the first and
second resonant frequencies [280].Most micromachined gyroscopes are based on vibration.
Vibratory gyroscopes use the transfer of energy between two
vibration modes by the Coriolis force. Micromachined gyro-
scopes are difficult to manufacture, as they require a high
performance resonator and an accelerometer, coupled in a
high-vacuum hermetic package.
In most commercial MEMS gyroscopes, the same
transduction scheme is preferred for both resonatoractuation and acceleration sensing for ease of integration,
e.g., piezoelectric or capacitive; this is one reason why
piezoresistive gyroscopes are not seen in production.
Another reason is the 1/f noise source. In most rate sensing
applications, i.e., navigation, the primary variable of
interest is position. However, a gyroscope senses rate of
rotation and to obtain position the output of gyroscope
must be integrated. As with any integration, the slightestoffset errors will induce an increasing (ramped) error in
the integrated position. Hence, the zero stability and 1/f
noise of gyroscopes are of enormous importance for
position sensing applications. Piezoresistor transduction
has inherent 1/f noise that limits the useful integration
time (accuracy) on the device output. Capacitive sensing
gyroscopes are more commonly employed because they do
not exhibit 1/f noise at the transducer. However, withprogress in very low 1/f noise piezoresistors [56], piezo-
resistive gyroscopes may soon appear with new possibil-
ities of improved quadrature signal cancellation.
3) Shear Stress Sensors: The accurate measurement of
wall shear stress (or skin friction) is important for both
applied and basic problems. From improving the aerody-
namic design of a vehicle body to understanding theformation of atherosclerosis on the wall of human blood
vessels [281], shear stress measurement provides key input to
understanding the fluid flow physics. Naughton and Sheplak
reviewed three relatively modern categories of skin-frictionFig. 27. A MEMS gyroscope is driven in one axis and
sensed in an orthogonal axis.
Fig. 28. Gyroscope with electromagnetic excitation and
piezoresistive detection. From Paoletti [278]. � 1996 IEEE.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 535
measurement techniques that are broadly classified asMEMS-based sensors, oil-film interferometry, and liquid
crystal coatings [282]. While MEMS-based techniques show
great promise, further development is needed and piezo-
resistive shear stress sensors are an area of active research
[282], [283]. Piezoresistive shear stress sensors commonly
utilize a floating-element anchored to the substrate via four
piezoresistive tethers (fixed-guided beams). The displace-
ment of the floating element due to the integrated shear stress(force) is detected as bending stress in the piezoresistors.
Ng et al. [284] and Shajii et al. [285] used wafer-bonding
technology to fabricate floating-element (120 � 140 �m2)
sensors. Piezoresistors were fabricated on the top surface of
the tethers using ion implantation (Arsenic at 80 keV and
7� 1015 cm�2 dose). In operation, the fluid flow direction
was parallel to the tethers such that a shear force over the
element loads two of the tethers in axial compressive stressand the other two in axial tensile stress. The sensor was
designed to detect high shear stresses (1–100 kPa) in high
pressure (6600 psi) and high temperature (220 �C) liquid
environments, and was tested in a cone-plate viscometer.
We used oblique (20�) ion-implantation to form piezo-
resistors on the sidewall of two tethers and a normal sur-
face implant for two other tethers (Fig. 29) [53]. The
sidewall piezoresistors are sensitive to lateral deflections(Fz and My in the flow direction), while the normal
piezoresistors are sensitive to flow fluctuations producing
out-of-plane deflections (Fy and Mz). Thus, each sensor
enabled simultaneous measurements of normal and shear
stresses. The floating element ð500� 500 �m2Þ was
defined using frontside and backside silicon DRIE pro-
cesses. A hydrogen anneal (1000 �C and 10 mTorr for
5 minutes) smoothed the DRIE scallops before ion-implantand improved the 1=f noise level of the oblique-implanted
piezoresistors by an order of magnitude. The sensors were
designed for harsh, liquid environments, and were tested in
a gravity-driven flume [150]. Li et al. also developed
piezoresistive shear stress sensors using oblique ion-
implantation technique, optimizing the geometry of the
piezoresistors and the sensors, as well as the dopant
concentration and bias voltage [125], [286]. Other piezo-resistive 3D stress sensors have been used to measure
multi-axis tactile or traction forces for biological [287]–
[289], robotic [290], and device packaging applications
[59]–[61], [69], [153], [291]–[294]. Noda et al. fabricated
2-D shear stress sensors for tactile sensing with standing
piezoresistive cantilevers embedded in polydimethyl-
siloxane (PDMS) [295]. Fan et al. and Chen et al. have
designed, fabricated, and characterized artificial-hair-cell-based piezoresistive flow sensors for underwater applica-
tions [296], [297]. These artificial haircells are inspired by
biological hair-cells and utilized arrays of piezoresistive
cantilevers with posts (hairs) normal to the cantilever. These
sensors can also be used to measure shear stress with similar
principles to those of piezoresistive fence-based shear stress
sensors [298], [299].
Fig. 29. (a) Piezoresistive floating-element MEMS shear stress sensor.
Each sensor consists of two top-implanted and two sidewall-implanted
piezoresistors. The sidewall-implanted piezoresistors are sensitive to
in-plane stress (shear stress), while the top-implanted piezoresistors
are sensitive to out-of-plane stress (normal stress). Thus, each sensor
enables simultaneous measurements of normal and shear stresses.
(b) SEM image of a 500-�m square floating element. (c) SEM image of
one of the tethers with a sidewall-implanted piezoresistor.
Reprinted from Barlian et al. [53] with permission from Elsevier.
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
536 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
E. Signal Conditioning andTemperature Compensation
As discussed in Sections II-D2 and II-E1, piezoresistors
are also sensitive to temperature variations. In many cases,
the resistance change due to temperature is higher than that
of the desired signal. The electronics can correct for these
changes. Moreover, processing variations also give rise to
different piezoresistive characteristics, which in turn alter
the temperature characteristics of each sensor. However,each piezoresistive sensor can be individually calibrated to
achieve high accuracy. The most common temperature
compensation techniques in piezoresistive sensors use
identical resistors in a Wheatstone bridge configuration.
Co-fabricated piezoresistors of the same design exhibit
similar temperature dependence; therefore, the zero output
of a compensated Wheatstone bridge remains constant with
temperature changes (to first order). This scheme trades offfavorably for signal-to-noise ratio (SNR) with increased
sensitivity despite increased noise e.g., Mallon et al. [56].
Temperature-sensing resistors may also be co-fabricated
with stress-sensing piezoresistors and used as bridge
elements. These resistors should be placed near one another
to minimize the effects of process variation. Modern
electronics can ultimately correct all repeatable errors. If a
piezoresistive sensor is heated and then cooled to the initialtemperature, then the output should be the same for the
same input. However, small differences are observed
between temperature cycles. This thermal non-repeatability
is one of the fundamental limits of sensor accuracy, not
correctable with signal conditioning circuits.
Prior to 1980 most of the temperature compensation
circuits for piezoresistive sensors employed trim resistors
with or without low noise bipolar amplifiers. Laser-trimmedresistors are used to adjust the offset, span, nonlinearity and
other errors of piezoresistive sensors. Laser-trimmed ampli-
fiers are rather bulky due the mechanical limits placed on
the trim resistors. CMOS circuitry became the dominant
source of signal conditioning after 1990. The need for even
smaller, more accurate, and cheaper sensors was an impetus
for the transition to CMOS. The bipolar technology, an
analog technology, does not offer the functionality of adigital technology (CMOS) measured in terms of cost per
power per functionality. The push toward CMOS technology
evolved with the availability of non-volatile memory (NVM).
The laser-trimmed resistors were then replaced with digital-
to-analog converters (DAC) and memory. By use of double
correlated sampling, offset and low frequency noise of the
CMOS circuit are sampled and stored on a capacitor and in
the next cycle they are subtracted from the original signal.Hence rendering the CMOS amplifier almost ideal in the
low frequency region relative to the sampling frequency. In
CMOS, the need for digital output is easily addressed by
integrating the analog to digital converter with the sensor. A
majority of designs incorporate sigma-delta converters
(Fig. 30) as the primary analog to digital converter (ADC)
architecture due to its inherent robustness [300], [301].
By use of analog circuit techniques and NVM, the needfor laser trimming as a means of sensor compensation was
eliminated and the power of digital technology was used to
compensate and calibrate the piezoresistive sensors. This
technology enabled unprecedented sensor accuracy at very
low cost [302].
There are two main architectures for piezoresistor
temperature compensation, i.e., fully digital path and
digitally controlled analog path [303]. Digital path archi-tecture uses an ADC to digitize the sensor and temperature
signal and then uses a mathematical equation to compen-
sate offset and span. If an analog output is needed then the
compensated digital data is fed to a DAC. This architecture
is the most flexible but has some inherent problems that
limit its use in control loops. One of the main drawbacks is
the delay time from the input to output. The ADC, the
microprocessor, and the DAC all need processing time, thisdead time may not be tolerated in feedback control. In
contrast, the analog path architecture takes advantage of
the fact that temperature is a slow signal. Hence, delay in
processing of the temperature signal is not of concern. The
digitized temperature signal is mathematically processed
and controls an analog path by changing the gain and the
offset of wide-band amplifiers, which inherently have small
delays.The question of integration of the sensor with elec-
tronics mainly depends on the application. Generic signal
conditioning circuitry consists of an excitation circuit, a
bridge circuit, an amplifier, and a filter [51]. These compo-
nents all contribute to the overall resolution of the system
(Fig. 31). Ishihara et al. developed the first CMOS inte-
grated silicon diaphragm pressure sensors in 1987 [304].
Since then, CMOS circuitry has been integrated with pie-zoresistive MEMS devices, such as AFM [63], [195], [205],
[216], [219], [305]–[307] and force or stress sensors [59],
[61], [68], [290], [292], [294], [308]–[310]. Mayer et al.determined three piezoresistive coefficients, �11, �12, and
�44, of an nþ diffusion of a commercial piezoresistive
CMOS chip using a novel method by subjecting the chip to
three different stress fields [311]. This method can be used
to calibrate CMOS-based piezoresistive stress sensor chips.Baltes et al. reviewed advances in the CMOS-based MEMS
until 2002, including microsensors and packaging, and
discussed some key challenges and applications for the
future [312], [313]. Recently, more advanced techniques
have been employed to achieve better control in tempera-
ture compensation. Chui et al. took advantage of the
dependence of the piezoresistive coefficient of silicon on
crystallographic orientation, and showed an order of mag-nitude improvement in thermal disturbance rejection over
conventional approaches using uncoupled resistors by using
piezoresistors in both the h100i and h110i directions [314].
Mallon et al. used a modulation-demodulation circuit
to measure 1=f noise of piezoresistors at low frequencies
[56]. The modulation demodulation technique is primarily
used for low noise and low frequency detection of a sensor
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 537
signal. This technique overcomes the high noise of
electronics at low frequencies since all linear non-switched
electronic amplifiers exhibit higher noise at low frequen-
cies. The bridge is excited with sinusoidal voltage (10 Vpp).
The output of the piezoresistive bridge is proportional
to the applied voltage multiplied by conductivity variation.
The modulated output of the piezoresistive bridge is thenamplified (�1000) using a high frequency low noise
amplifier (TI103), and then bandpass-filtered to reduce the
effect of noise folding (bandwidth �200 Hz, center
frequency 500 Hz). Using a multiplier with gain of 4=�(AD630) the signal is demodulated. The signal is finally
low-pass filtered with a three pole filter (Fig. 32).
F. Device Design SummarySince the discovery of piezoresistance, several genera-
tions of commercial device designers and academic re-
searchers have designed piezoresistive sensors for diverse
applications. However, all piezoresistive sensors have
fundamental tradeoffs between sensitivity and noise. The
piezoresistor geometry, device geometry, and fabricationprocess must be designed together for low noise and high
sensitivity to achieve the required resolution. Design
constraints and flexibility have evolved with mainstream
Fig. 31. The power spectral density (PSD) and integrated force noise of
a measurement system using an AD622 instrumentation amplifier and
piezoresistor bridge. All components in a signal conditioning circuit
contribute to the noise and resolution of the system. Courtesy
of Sung-Jin Park [54], reprinted with permission from PNAS.
Fig. 30. (a) CMOS integrated piezoresistive cantilever array (two scanning cantilevers and one reference cantilever) (b) Micrograph of the overall
sensor CMOS signal conditioning circuit (c) Array of 12 cantilevers (the inner ten can be used for scanning while the outer two serve as a reference).
The dimensions of the scanning cantilevers are 500 �m� 85 �m. From Hafizovic et al. [305], reprinted with permission from PNAS.
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
538 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
semiconductor technology providing new processes such
as ion implantation and reactive ion etching. As discussed
already, several investigators have provided detailed device
optimization analyses for given applications within very
specific constraints [46], [57], [149], [181]–[183], [213],[262]. No concise, generic design guidelines exist for all
devices types and the sensitivity and noise are convolved
with the geometry and mechanics of any particular device.
However, the design criteria for the piezoresistor itself can
be described by a rich parameter space and we review here
many that are directly in control of the designer.
Design parameters include: dopant type, energy, and
deposition method; the type, temperature and time ofanneal(s); the thickness ðtpÞ, length ðlpÞ, and width ðwpÞ of
the piezoresistor and their relation to device geometry
(e.g., ratio of piezoresistor length to beam length); and the
number of dopant atoms ðNÞ in the piezoresistor volume.
The geometry and dimensions of the device are designed in
parallel to meet bandwidth, dynamic range, sensitivity,
and resolution requirements. Particular attention to the
tradeoffs in parameters is required when pushing towardsvery small sizes, high sensitivity, or large bandwidth.
Figs. 12, 15, and 18 and (13) and (14) provide quantitative
guidance in the tradeoffs in selecting dopant concentra-
tion, anneal, and bias voltage to increase sensitivity and
decrease noise. For example, the minimum force resolu-
tion in an ion implanted, end-loaded, piezoresistive canti-
lever in a 1/4-active Wheatstone bridge may be expressed
as a function of (11), (12), (15), and (16) as
Fmin¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2
bias
2lpwpNzln fmax
fmin
� �þ8kBTRs
lpwpðfmax�fminÞ
r
3 l�12lpð Þ�l max
2wt2 �� Vbias
(19)
where is the ratio of the strained region of piezo-
resistance to the unstrained resistance path.
However the optimization must also be tempered with
application specific requirements for device size, power
dissipation, bandwidth, dynamic range, linearity, and tem-perature stability. For example, reduced power dissipation
argues for higher overall resistance (lower N) and lower bias
voltage. Lower carrier number ðNÞ concomitantly increases
the 1=f noise, resistance, sensitivity, temperature coeffi-
cients of sensitivity and resistance, while higher resistance
increases Johnson noise. In determining dimensions for a
displacement sensing cantilever, Table 3 provides a rela-
tional matrix between parameters the designer can tune totailor device performance.
Generally, larger dimensions allow better sensitivity
and larger piezoresistor size which lowers noise and im-
proves heat dissipation. Beam dimensions are selected for
dynamic range, sensitivity, and bandwidth. Minimum
thickness is limited by process capability (Section III-C)
and should also be selected to achieve appropriate piezo-
resistor strain and account for strains from residualstresses in dielectrics or thin films. Well-prepared, small-
diameter samples of silicon exhibit high fracture stress
[315], while processed MEMS devices of millimeter di-
mensions exhibit lower values [316].
Once devices are fabricated, testing usually involves
characterization of noise power spectral density and sensi-
tivity calibration of individual devices after packaging and
integration with signal conditioning. The noise integratedover the measurement or application frequency band sets
the resolution, reported by converting voltage output to
the measurand using the sensitivity calibration. Calibra-
tion methods vary from device to device but should be
accomplished over the temperature range, dynamic range,
and bandwidth appropriate to the application. For exam-
ple, piezoresistive cantilevers calibrated with an electro-
static force balance at the U.S. National Institute ofStandards and Technology (NIST) are promising metrol-
ogy devices as force transfer standards for MEMS and AFM
users [317], [318].
IV. ALTERNATIVE PIEZORESISTIVEMATERIALS
Most commercial and research piezoresistive MEMSdevices and microsystems utilize silicon and germanium,
or their alloys. For example, Lenci et al. reported the first
experimental values of piezoresistive coefficients in
polycrystalline silicon-germanium and demonstrated a
pressure sensor of this material [319]. They found
longitudinal and transverse piezoresistive coefficients of
4:25� 10�11 Pa�1 and 0:125� 10�11 Pa�1, respectively.
However, with advances in materials science and proces-sing, newer materials are currently being developed for
MEMS and microsystems. These materials have advan-
tages over silicon in some applications (e.g., higher melting
temperature, higher/lower modulus of elasticity, or higher
piezoresistive coefficients). In this section, we review four
novel materials that could complement silicon in piezo-
resistive sensing applications.
Fig. 32. Modulation-demodulation circuit for low frequency low
noise detection.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 539
A. Silicon CarbideSilicon Carbide (SiC), with superior mechanical prop-
erties, such as higher Young’s Modulus (424 GPa), higher
sublime temperature (1800 �C), higher thermal conductiv-
ity, and inertness to corrosive environments, is an attractive
new material for MEMS and NEMS devices [320]. In addi-
tion to its superior mechanical properties, single crystal SiC
also has a wider band gap (2.39–3.33 eV) compared to that ofsingle crystal silicon (1.12 eV) [320]. This reduces the effect
of thermal generation of carriers that results in increased
reverse leakage current across a p-n junction, at high tem-
peratures. Werner and Fahrner summarized electronic
maximum operating temperature and band gaps for several
semiconductor materials [321]. SiC has several advantages
over other wide-bandgap materials (GaAs, diamond, etc.),
including commercial availability of substrates, some deviceprocessing techniques, and the ability to grow stable native
oxides [320]. Nevertheless, obtaining a high-quality oxide
with low interface state and oxide trap densities has proven
challenging because of the carbon on the surface, as well as
off-axis epitaxial layers which have rough surface morphol-
ogies [322].
SiC has about 200 known polytypes. The physical
properties of each polytype vary. A complete review of SiCcrystal structures and polytypes is available elsewhere
[323]. The most common ones are 6H-SiC, 4H-SiC, and
3C-SiC. Polytypes 6H-SiC and 4H-SiC have a hexagonal
crystal structure (-SiC), while 3C-SiC has a cubic crystal
structure (�-SiC). In one of the earliest systematic studies
in the piezoresistivity of 3C-SiC, Shor et al. measured
the longitudinal and transverse gauge factors as a function
of temperature for two different doping levels [324].
Ziermann et al. reported the first piezoresistive pressure
sensor using single crystalline �-SiC n-type piezoresistors
on Silicon-on-Insulators (SOI) substrates [325]. Studies
performed on the piezoresistivity of a-SiC have shown
negative gauge factors as large as �35 for longitudinal
and �20 for transverse gauge factors [326], [327]. A
summary of published piezoresistive data for both - and
�-SiC through 2001 was presented by Werner et al.(Fig. 33) [328].
In contrast to its single crystal counterpart, polycrys-
talline SiC exhibits positive gauge factors of smaller
magnitude. Strass et al. provided a summary of the gauge
factor of polycrystalline SiC as a function of temperature
and doping [329]. At room temperature, the gauge factor is
around 6 for undoped and 2–5 for doped polycrystalline
SiC. The shift from negative to positive values wasexplained by the greater influence of grain boundaries in
polycrystalline wide-bandgap materials compared to poly-
silicon. The piezoresistance also depends on the temper-
ature, the crystal orientation, and the doping type.
Piezoresistance of polycrystalline �-SiC fibers has also
been studied [330]. With a gauge factor of 5 in 14-�m
diameter �-SiC fibers under tension, SiC fibers have been
used for continuous reinforcement of high-temperaturestructural composites for their oxidation resistance. Their
piezoresistive properties are useful to monitor strain in
these composites.
Additionally, theoretical investigations of the piezore-
sistivity in the cubic 3C-SiC and hexagonal n-type 6H-SiC,
based on electron transfer and the mobility shift mecha-
nism, have been performed [331], [332]. In the hexagonal
6H-SiC, the anisotropic part of the piezoresistance tensor
Table 3 Example Design Matrix Showing Relationship of Parameters in Piezoresistive Cantilever Beam for Displacement Sensing [Trends Within the
Ranges of Figs. 12, 15, 16 and 18 and (13) and (14)]. As the Controlled Design Parameter Increases (While Other Parameters Are Held at Typical Values and
Input Displacement is Fixed), the Observed Parameters Respond as: Increasing ð"Þ, Decreasing ð#Þ, Weak or No Relation ð�Þ. Note: ð�Þ Please See Fig. 15.
Vb, Vb, and Dt are the Dopant Concentration, Bias Voltage, and Diffusion Length, Respectively. tp, wp, and lp are the Piezoresistor Thickness, Width, and
Length, Respectively. h, b, and L are the Cantilever Beam Thickness, Width, and Length, Respectively
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
540 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
vanishes in the (0001) plane and only the isotropic part
remains. As a consequence, longitudinal, transverse, and
shear gauge factors and properties are isotropic in the
(0001) plane.Several SiC-based piezoresistive MEMS devices have
been developed to withstand harsh operating environ-
ments, such as high impact/acceleration (40 000g) [333]
and high temperatures (200–500 �C) [334]–[336]. Com-
plete reviews of SiC-based MEMS and NEMS, especially
for harsh environment applications, are available else-
where [321], [328], [337]–[340].
B. DiamondDiamond is also an attractive new material for micro-
mechanical devices for elevated temperatures and harsh
environments [321], [328], [341], [342]. Superior proper-
ties, compared to silicon, include physical hardness, higher
Young’s modulus, higher tensile yield strength, greater
chemical inertness, lower coefficient of friction, and higher
thermal conductivity. Experimental values for Young’smodulus of CVD diamond have been reported from 980 to
1161 GPa [341].
Doping of diamond can be done in-situ during film
growth, or using other standard techniques, such as ion
implantation and high-temperature diffusion. Werner et al.summarized both longitudinal and transverse piezoresis-
tive coefficients reported by various research groups before
1998 (Fig. 34) [342]. The reported piezoresistive GF ofsingle crystal and poly-crystalline diamond are typically in
the ranges of 2000–3836 and 10–100, respectively [343].
Polycrystalline diamond has a higher GF compared to that
of SiC, but like the other piezoresistive properties, these
values depend greatly on the doping concentration and
temperature.
The relatively low GF of polycrystalline diamond isusually attributed to its polycrystalline structure. A study of
intra- and inter-grain conduction in large-grain CVD
diamond showed the intra-grain resistivities are lower
than those of grain boundaries [343]. The intra-grain GF
over 4000 for a large grain (50–80 �m) polycrystalline
diamond is the largest piezoresistive effect reported for any
material. However, the GF deteriorates when grain
boundaries are included in the conductance path, with aGF of 133 when the conductance path includes eight grain-
boundaries. Yamamoto and Tsutsumoto suggested two
methods to improve the GF of polycrystalline diamond
films [344]. The first was to decrease the ratio of carbon to
hydrogen when depositing boron-doped diamond films.
Decreasing the ratio of C-O/H from 5.5% to 2.2%,
increased the GF from 3 to 30. In this case, the quality
of diamond was improved by decreasing the C-O/H ratioand the GF increased as the diamond quality was improved
and the grain size became larger. A second method varied
boron doping time and the boron-doped layer thickness.
Varying doping time from 3 to 10 minutes (corresponding
to layer thickness of 0.1 to 0.33 �m) increased the GF from
0 to 50.
C. Carbon Nanotubes (CNT)Carbon nanotubes (CNTs) are graphene sheets rolled-
up into cylinders with diameters as small as one nanometer
and lengths as large as centimeters. This form of carbon
was first reported by Iijima in 1991 [345]. Mechanically,
nanotubes are among the strongest and most resilient
materials known in nature. CNT Young’s modulus is on the
order of TPa with tensile strength two orders of magnitude
higher than that of steel [346]. Electronically, CNTs canbe metallic, semiconducting, or small-gap semiconducting
(SGS) [347]. Qian et al. reviewed theoretical predictions and
Fig. 34. The summary of published average longitudinal and
transverse piezoresistance coefficients in boron-doped polycrystalline
diamond by Werner et al. [342]. The published gauge factor data were
converted to piezoresistive coefficients assuming Young’s modulus of
1143 � 109 Pa. After Werner et al. [342]. � 1998 IEEE.
Fig. 33. Longitudinal gauge factor in h100i direction for �-SiC as a
function of temperature for different doping levels from various
researchers [324], [325]. Werner et al. noted that these experimental
data are in good agreement with the theoretical gauge factor predicted
by electron transfer mechanism theory [81] in many-valley
semiconductors [328]. After Werner et al. [328]. Reprinted with
permission from Wiley.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 541
experimental techniques that are widely used for visualiza-tion, manipulation, and measurements of mechanical
properties of CNTs [348]. Most experiments use an AFM
tip to deflect a CNT suspended over a trench and several
experiments have measured electromechanical properties of
CNTs [349]–[351]. The piezoresistance is attributed to
energy band shifts and is observed as a shift in nonlinear
CNT I-V curves. Fung et al. integrated bundled strands of
CNT on polymer-based diaphragms of microfabricatedpressure sensors using dielectrophoretic (DEP) nanoassem-
bly [352]. Grow et al. reported measurements of the elec-
tromechanical response of CNTs adhered to pressurized
membranes [353]. Single-tube CNTs adhered to silicon
nitride membranes by van der Waals interactions, were
electrically connected in-situ and assumed to experience the
same strain as the membrane (Fig. 35). The conductivity of
the CNT decreased as the membrane was pressurized (0 �15 psi). This CNT pressure sensor had a resolution of 1 psi
with CNT gauge factors of 400 and 850 for semiconducting
and SGS tubes, respectively. Possible applications include
integration of nanotubes on or in a variety of substrates,
including flexible plastics. Chiamori et al. [354] incorporated
single-wall nanotubes (SWNT) into the negative resist
material, SU-8, and investigated the SU-8/SWNT nano-
composite electromechanical properties, such as effectiveYoung’s modulus and piezoresistivity. We found a gauge
factor of 2–4 for the 1–5 wt% (weight percent) SU-8/SWNT
composite and an effective Young’s modulus of about
0.5 GPa for the 1 wt% composite. Complete reviews of
electromechanical properties and other applications of CNT
are available elsewhere [347], [355], [356].
D. NanowiresNanowires, also known as quantum wires, are electri-
cally conducting wires, in which quantum transport effects
are important. As the width of the wire is reduced to Fermi
wavelength scale, the conductance between the electrodes
connected by the nanowire is quantized in steps of 2e2=h(where e is the charge of the electron and h is the Planck’s
constant) and conductance is no longer dependent on the
length of the wire [357]. Different types of nanowires, e.g.,
metallic, semiconducting, insulating, and molecular (or-ganic and inorganic) have different electromechanical pro-
perties. Nanoindentation is a popular method to determine
the hardness and elastic modulus of nanowires, such as
gallium nitride (GaN) and zinc oxide (ZnO) nanowires,
tantalum oxide (Ta2O5) nanowires, single-crystal and poly-
crystalline copper nanowires, and gold nanowires [357]–
[362]. Zhu and Espinosa, Desai et al., and Lu et al. have also
developed MEMS experimental test beds for electro-mechanical testing of nanowires [359], [362], [363].
To date, relatively few reports on the development of
silicon nanowire-based sensors are available [364]. How-
ever, p-type single crystalline silicon nanowires have been
studied for sensor applications [365], [366]. Separation by
implanted oxygen (SIMOX), thermal diffusion, electron
beam (EB) direct writing, and reactive ion etching (RIE)
have been used to fabricate silicon nanowire piezoresistors[365]. Both the longitudinal and transverse piezoresistive
coefficients, �l½011� and �t½011�, are dependant on the cross
sectional area of the nanowires. The �l½011� of the nanowire
piezoresistors increased (up to 60%) with a decrease in the
cross sectional area, while �t½011� decreased with a de-
crease in the cross sectional area (Fig. 36). The enhance-
ment behavior of the �l½011� was explained qualitatively
using 1-D hole transfer and hole conduction mass shiftmechanisms. The decrease in the �t½011� with decrease in
the cross sectional area is due to decrease in the stress
transmission from substrate to the nanowire. The maxi-
mum value, �l½011� of 48� 10�11 Pa�1 at a surface con-
centration of 5� 1019 cm�3, suggests enough sensitivity for
sensing applications. Dao et al. incorporated these p-type
silicon nanowires as piezoresistive elements in a miniatur-
ized 3-degrees-of-freedom (3-DOF) accelerometer [367].
Fig. 35. (a) Schematic of a CNT device on a membrane (b) Optical
microscope image of a membrane with electrodes (c) Zoomed in image
of devices near the edge of a membrane (d) SEM Image of a CNT
crossing the gap between two electrodes (�800 nm). Reprinted with
permission from Grow [353]. � 2005 American Institute of Physics.
Fig. 36. Size (cross sectional area) effect on longitudinal and
transverse piezoresistive coefficients in boron-doped nanowires
fabricated using electron beam (EB) lithography and
reactive-ion-etching (RIE). After Toriyama [366]. � 2002 IEEE.
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
542 Proceedings of the IEEE | Vol. 97, No. 3, March 2009
Roukes and Tang patented strain sensors based on
cantilever-embedded nanowire-piezoresistor wires and
ultra-high density free-standing nanowire arrays [368].
He and Yang reported on very large piezoresistance
effect (commonly referred to as ‘‘giant piezoresistance’’) in
p-type silicon nanowires, particularly in the h111i direction
[369]. The measured piezoresistance values were a function
of the nanowires diameters and resistivities, with the largestvalue of �3550� 10�11 Pa�1 in the longitudinal direction.
Silicon nanowires in the h111i direction, with diameters of
50–350 nm and resistivities of 0.003–10 � cm, were grown
and anchored to a silicon substrate (from SOI wafers) to
form a bridge structure (Fig. 37) and uniaxial stress was
applied to the nanowires using a four-point bending setup.
Cao et al. explained the giant piezoresistance phenomenon
in h111i silicon nanowires based on a first-principles density-functional analysis and identified ‘‘the strain-induced bandswitch between two surface states, caused by unusual relaxationbehavior in the surface region,’’ as the key contributor [370].
Their model and calculations captured all the main features
of the experimental results by He and Yang. Following
the experimental results from He and Yang, Reck et al.used a lift-off and an electron beam lithography (EBL)
technique to fabricate silicon test chips and study thepiezoresistive properties of crystalline and polycrystalline
nanowires as a function of stress and temperature [371].
Compared to the bulk silicon’s piezoresistive effect, they
found a 633% and 34% increase in piezoresistive effect for
the crystalline and polysilicon nanowires, respectively. They
also found that the piezoresistive effect greatly increases as
the nanowire diameter decreases, consistent with the
results from He and Yang [369].
V. CONCLUSION
With the discovery of the large piezoresistive coefficients in
silicon in 1954, the study of piezoresistance moved from
scientific inquiry of a material property to extensive
investigation, development and commercialization. Piezo-
resistor development largely followed that of the main-stream semiconductor industry. Integration of piezoresistors
with micromachined flexure elements enabled widespread
implementation of these MEMS sensors. Piezoresistance has
become a fundamental sensing modality in the toolbox of
MEMS sensor designers. Recent research focuses on driving
to the nanoscale, using high band gap semiconductors to
make high pressure, high temperature sensors, and applying
piezoresistive cantilevers to biological and chemical sensing.Building on over fifty years of research, the field remains
active and vibrant. h
Acknowledgment
The authors are grateful to Dr. M. A. Hopcroft,
Dr. M. Doelle, P. Ponce, N. Harjee, S.-J. Park, and P. Lim
for helpful discussions.
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ABO UT T HE AUTHO RS
A. Alvin Barlian received the B.S. degree with Honors and
Distinction from Purdue University, West Lafayette, IN, in 2001
and the M.S. and Ph.D. degrees from Stanford University,
Stanford, CA, in 2003 and 2009, respectively, all in mechanical
engineering.
His doctoral research focused on the development of micro-
fabricated piezoresistive shear stress sensors for harsh liquid
environments, characterization of microfabricated piezoresistive
cantilevers for force sensing applications, and a novel sidewall
epitaxial piezoresistor fabrication process for in-plane force
sensing applications (U.S. patent, pending). In 2008, he worked on the characterization
of capacitive RF MEMS switches as an Interim Engineering Intern with the Technology
R&D Department at Qualcomm MEMS Technologies.
In 2007, he was presented the Centennial Teaching Assistant Award by Stanford
University for his efforts in co-developing a micro/nanofabrication laboratory course at
Stanford University. In 2005, he received the Best Poster Award for the most outstanding
poster presentation at the International Mechanical Engineering Congress and
Exposition in Orlando, FL. In 2001, he was inducted into the Honor Society of Phi Kappa
Phi and he received the John M. Bruce Memorial Scholarship from Purdue University. He
was the P.T. Caltex Pacific Indonesia scholar from 1998 to 2002.
Barlian et al. : Review: Semiconductor Piezoresistance for Microsystems
Vol. 97, No. 3, March 2009 | Proceedings of the IEEE 551
Woo-Tae Park received the B.S. degree in
mechanical design from Sungkyunkwan Univer-
sity, Seoul, Korea, in 2000, the M.S. and Ph.D.
degrees in mechanical engineering from Stanford
University, Stanford, CA, in 2002 and 2006
respectively.
For his graduate degree work, he worked on
optical measurements for electrical contact defor-
mation, wafer scale encapsulated MEMS devices,
and submillimeter piezoresistive accelerometers
for biomedical applications. After graduation, he started as a senior
packaging engineer at Intel, designing silicon test chips for assembly, test,
and reliability. He is nowwith Freescale semiconductor, working onMEMS
process development in the Sensor and Actuator Solutions Division.
Dr. Park has authored seven journal papers, fifteen conference papers
and holds one patent.
Joseph R. Mallon, Jr. received the B.S. degree in
science (cum laude) from the Fairleigh Dickinson
University and the MBA degree in Management,
Marketing and New Venture from California State
University, Hayward, CA. From 1965 to 1985,
Mr. Mallon was the Vice President of Engineering
for Kulite Semiconductor Products, one of the
earliest MEMS sensor companies. From 1985 to
1993, he was the Co-President, COO, Co-Founder,
and Director of NovaSensor, a venture funded
Silicon Valley firm that helped establish MEMS as a widely known and
commercial technology. Mr. Mallon was the Chairman and CEO of
Measurement Specialties, a publicly traded sensor manufacturer, from
1995 until 2002. Currently he is studying and doing research at Stanford
University along with his position as the CEO of axept. Mr. Mallon is a
pioneer in MEMS technology with forty-five patents and over sixty
technical papers and presentations.
Ali J. Rastegar received the B.S. and M.S. degrees
in electrical engineering from the Worcester
Polytechnic Institute in 1982 and 1984, respec-
tively. He then joined Analog Devices as an
integrated circuit design engineer where he
developed several high-speed, state of the art
analog-to-digital converters. In 1992, he founded
MCA-technologies which was purchased by
Maxim integrated products in 1997. In 2001
Mr. Rastegar became fascinated with the infor-
mation storage capabilities of living cells and decided to further his
understanding by pursuing the Ph.D. degree and joining the Stanford
Microsystems Laboratory. Mr. Rastegar has designed more than
54 integrated circuits and holds eight issued U.S. patents.
Beth L. Pruitt (B.S. MIT 1991, M.S. 1992 and Ph.D.
2002 Stanford University) developed Piezoresis-
tive Cantilevers For Characterizing Thin-Film Gold
Electrical Contacts during her Ph.D. In 2002 she
worked on nanostencils and polymer MEMS in the
Laboratory for Microsystems and Nanoengineer-
ing at the Swiss Federal Institute of Technology
(EPFL). She joined the Mechanical Engineering
faculty of Stanford in Fall 2003 and started the
Stanford Microsystems Lab. Her research in-
cludes piezoresistance, MEMS and Manufacturing, micromechanical
characterization techniques, biomechanics of mechanotransduction,
the development of processes, sensors and actuators as well as the
analysis, design, and control of integrated electro-mechanical systems.
Her research includes instrumenting and interfacing devices between
the micro and macro scale, understanding the scaling properties of
physical and material processes and finding ways to reproduce and
propagate new technologies efficiently and repeatably at the
macro-scale.
Prior to her Ph.D. at Stanford, Beth Pruitt was an officer in the U.S.
Navy, at the engineering headquarters for nuclear programs and as a
Systems Engineering instructor at the U.S. Naval Academy, where she
also taught offshore sailing.
Barlian et al.: Review: Semiconductor Piezoresistance for Microsystems
552 Proceedings of the IEEE | Vol. 97, No. 3, March 2009