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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 26, NO. 5, OCTOBER 2017
Thermoresistive Effect for Advanced Thermal
Sensors: Fundamentals, Design Considerations,
and Applications
Toan Dinh, Hoang-Phuong Phan, Afzaal Qamar, Peter Woodfield, Nam-Trung Nguyen, and Dzung Viet Dao
Abstract— Microelectromechanical systems sensors have been
intensively developed utilizing various physical concepts, such as
piezoresistive, piezoelectric, and thermoresistive effects. Among
these sensing concepts, the thermoresistive effect is of interest
for a wide range of thermal sensors and devices, thanks to
its simplicity in implementation and high sensitivity. The effect
of temperature on the electrical resistance of some metals and
semiconductors has been thoroughly investigated, leading to the
significant growth and successful demonstration of thermal-based
sensors, such as temperature sensors, convective accelerometers and gyroscopes, and thermal flow sensors. In this paper,
we review the fundamentals of the thermoresistive effect in metals
and semiconductors. We also discuss the influence of design and
fabrication parameters on the thermoresistive sensitivity. This
paper includes several desirable features of thermoresistive sensors and recent developments in these sensors are summarized.
This review provides insights into how it is affected by various
parameters, and useful guidance for industrial designers in terms
of high sensitivity and linearity and fast response. [2017-0022]
Index Terms— Thermoresistive effect, semiconductor, metal,
two-dimensional (2-D) material, thermal sensor, temperature
sensor, thermal flow sensor, convective accelerometer, gyroscope.
I. I NTRODUCTION
F
OR MORE than three decades, MEMS (Micro ElectroMechanical Systems) sensors have been developed aiming
at high sensitivity, fast response, stability and reproducibility,
miniaturization capability and mass production. The working
principle of these sensors is based on a variety of physical
phenomena such as thermoresistive, piezoresistive, pseudohall, thermoelectric and piezoelectric effects [1], [2]. Among
these effects, the thermoresistive effect, which refers to the
electrical resistance change with temperature variation, has
many advantages in terms of simplicity in design and implementation. Based on this effect, various micro-sized thermal
sensors, which can monitor temperature [3], flow [4], [5] and
acceleration [6], [7], have been successfully fabricated, thanks
to the advancement in MEMS technologies.
Manuscript received January 26, 2017; revised April 26, 2017; accepted
May 26, 2017. Date of publication June 12, 2017; date of current version
September 29, 2017. Subject Editor P. M. Sarro. (Corresponding author:
Toan Dinh.)
T. Dinh, H.-P. Phan, A. Qamar, D. V. Dao, and N.-T. Nguyen
are with the Queensland Micro-Nanotechnology Centre, Griffith University, Nathan, QLD 4111, Australia (e-mail: toan.khac.dinh@gmail.com;
toan.dinh@griffithuni.edu.au).
P. Woodfield is with the Griffith School of Engineering, Griffith University,
Nathan, QLD 4111, Australia.
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JMEMS.2017.2710354
To date, a number of thermal sensing materials have been
employed for developing thermal sensors, including metals (e.g. platinum and nickel) and semiconductors (e.g. silicon
and polysilicon) [5], [8]. For example, platinum has been
used for constructing thermal flow sensors, owing to its linear
thermoresistive response, compatibility with microelectronic
technologies and relatively high positive temperature coefficient of resistance (TCR) [8]. In addition, semiconductors
could also be deployed for thermal sensors, thanks to their
wide range of TCR values from positive to high negative.
Interestingly, the TCR of semiconductors can be tuned using
different doping levels [9] or changing growth parameters [10].
However, the fabrication of these sensors, which requires
expensive materials, clean room facilities and specialized wafer processing equipment, has increased their cost,
especially for small-scale production [11], [12]. Moreover,
the fabrication of thermal flow sensors have involved various
solvents and chemicals which are unfriendly for the environment and could lead to contamination issues. In addition, these
sensors are unable to work in harsh conditions such as hightemperature and corrosive environments. Therefore, there is
a strong demand for investigating alternative novel thermal
sensing materials for advanced thermal sensors. Desirable
characteristics for these sensors would be (1) low cost and
high sensitivity, (2) linear response, stability and sustainability,
(3) capability of working in harsh environments such as at
high temperatures and (4) flexibility and suitability for a wide
range of applications, including the emerging field of wearable
applications.
The present paper reviews the fundamentals of the themoresistive effect (Figure 1, top-left), and the impact of design
and fabrication parameters on its sensitivity (Figure 1, topright). The desirable features for thermoresistive sensors such
as sensitivity, linearity and response time are also mentioned
(Figure 1, bottom-right). In addition, the applications of this
effect for thermal sensors, including temperature sensors, thermal flow sensors and convective accelerometers/gyroscopes,
are presented (Figure 1, bottom-left). Finally, current trends
and perspectives for the development of the thermoresistive
effect and its applications are discussed. This review provides useful design guidance to engineers and researchers
who are working on the development of thermal sensors.
Following, section 2 revisits the fundamental aspects of thermoresistive effects, including those in semiconductors and
metals. Section 3 discusses the impact of design and process
1057-7157 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
DINH et al.: THERMORESISTIVE EFFECT FOR ADVANCED THERMAL SENSORS
967
Fig. 1. A brief overview of the thermoresistive effect, its design parameters, desirable features and applications. “Materials”: Reproduced from [34] and [36]
with permission from the Royal Society of Chemistry and Elsevier.
on the performance of thermoresistors. The key parameters
are the doping concentration, the material and morphology,
the deposition temperature, the grain size and thickness.
Section 4 considers the desirable features for thermoresistive
sensors, including sensitivity, linearity, time response, power
consumption and stability. Finally, section 5 discusses typical
applications of the thermoresistive effect such as temperature
sensing, flow sensing and acceleration sensing.
the temperature difference; T and T0 are the absolute temperature and reference temperature (normally room temperature),
respectively. Moreover, the change in the electrical resistance
caused by the influence of the change in the surrounding
temperature is known as the thermoresistive effect. In addition,
the resistance change under the effect of temperature variation
is attributed to the geometric effects (αT ) and the change in
resistivity (ρ/ρ) [14]:
II. F UNDAMENTALS OF T HERMORESISTIVE E FFECT
ρ
R
=
− αT
R
ρ
In general, the electrical resistance of a homogeneous
bar or film can be expressed in terms of its resistivity and
geometry as follows:
R=ρ
l
wt
(1)
where R and ρ are the electrical resistance and resistivity of
the material, respectively; l, w and t are the length, width and
thickness of the bar/film, correspondingly. Based on Eq. 1,
the resistance change (in the limit of small changes) can
be calculated depending on the resistivity change and the
dimension changes [13], [14]:
ρ
l
w t
R
=
+
−
−
R
ρ
l
w
t
(2)
The change in each dimension (e.g. length, width and
thickness), under a temperature variation, is the same because
of the homogeneous property of the material. This depends
on the thermal expansion coefficient (TEC, α) of the bar/film
as l/l = w/w = t/t = αT , where T = T − T0 is
(3)
For common metals, while the change in resistivity ranges
from 3,900 to 6,800 ppm/K, the geometric effects alone
contribute to the TCR less than 30 ppm/K [5], [15]. Therefore,
the error in neglecting geometric effects is less than 0.61 %
(see Table I). Moreover, for bulk semiconductors, the contribution of geometric effects to the TCR is less than 5 ppm/K and
the resistivity change depends upon various parameters such
as doping levels, morphologies and temperature ranges. It is
important to note that the temperature ranges also influence
the TCR of metals. The common value of TCR for bulk
semiconductors used for thermal sensing applications is from
several thousands to several ten thousands ppm/K [5], [15]. For
example, the geometry of silicon (TCR = -6,000 ppm/K [16])
contributes to 2.6 ppm/K, corresponding to an error of 0.04%.
Therefore, the geometric effects could be neglected when the
structure is employed for temperature sensing purposes. Thus,
the TCR is commonly defined as [13], [14]:
TCR =
ρ 1
R 1
=
R T
ρ T
or T C R =
1 dR
R dT
(4)
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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 26, NO. 5, OCTOBER 2017
TABLE I
R ESISTIVITY AND TCR OF M ETALS U SED IN T HERMAL -BASED S ENSORS , AND I MPACT OF T HERMAL E XPANSION ON TCR [5], [15], [89]
In addition, the resistivity and TCR of thin films also depend
upon their thickness. For example, when the thickness of the
film shrinks to the nanoscale (e.g. lower than 100 nm), its
resistivity increases significantly due to the increase in the
number of defects and boundaries in the film [17]. In addition,
the absolute TCR of thin-film semiconductors could also
increase with decreasing thickness because of the increase in
thermionic emission of the trapped carriers in the thin film at
elevated temperatures [17].
A high absolute TCR is desired for thermal sensing applications, since a sensor made of a high TCR material commonly
performs well, exhibiting corresponding high sensitivity. This
section first discusses thermoresistive principles and then
reviews the thermoresistive effect in common sensing materials such as metals, silicon and silicon carbide.
A. Thermoresistive Effect in Semiconductors
This section discusses the thermoresistive effect in silicon,
which can be extended to other semiconductors [1], [2]. The
thermoresistive effect arises because temperature affects the
number of carriers and their mobility in conducting materials.
In single crystalline materials, the number of free charge
carriers increases with the rise of temperature due to their
ability to be excited by thermal energy. This leads to an
improvement in electrical conductivity. However, the mobility
of the carriers decreases with increasing temperature due to
the scattering effect of lattice vibrations. Therefore, when the
temperature increases, the resistivity of the semiconductors
may decrease (negative temperature coefficient of resistance NTCR), or increase (positive temperature coefficient of resistance - PTCR), depending upon the change in the number of
carriers and their mobility. This dependence can be expressed
by [1], [2]:
1
= σ = enμe + epμh
(5)
ρ
where σ and e are the conductivity and electron charge,
respectively; n and p are the electron concentration and hole
concentration; respectively; μe and μh are the corresponding
electron mobility and hole mobility.
Figure 2 shows three temperature-dependent regions for
the resistivity of semiconductors. At sufficiently low temperatures (extrinsic region), more carriers (n ∼ T α ex p(E d /kT ),
where E d is the activation (ionization) energy of donors,
Fig. 2.
Temperature-dependent resistivity in semiconductors.
α is a constant and k is the Boltzmann constant, for
n-type Si, α = 3/2) would be generated by thermal energy
and excited to jump to the conduction band (CB). This is
apart from existing carriers, which would always contribute to
electrical conductivity. In addition, lattice scattering causes a
slight reduction of mobility (μ ∼ T −β , where β is a constant,
for extrinsic silicon β = 3/2). The combination of the carrier
concentration and mobility can lead to a decrease in electrical
resistivity (a negative TCR). Therefore, the electrical resistance
R of n-type semiconductors can be expressed in the following
form [1], [18]:
Ed
(6)
R = Aex p
kT
where A is a constant. The decrease in electrical resistivity in
the extrinsic region can be determined by a slope of E d /k.
However, at a higher temperature range (metal-like region),
the free carrier concentration is saturated while the carrier
mobility still decreases [19]. This region exhibits a positive
TCR. In addition, at the highest temperature range (intrinsic region), a significant number of bonds are being ruptured and the carrier concentration increases. As a result,
the temperature-dependent resistance of semiconductors is
E
commonly described as R = R0 ex p 2kTg , where E g is the
energy gap, and the slope of E g /2k defines the decrease of
resistivity in this region.
For semiconductor temperature sensors, the temperature
dependence of electrical resistance is generally used in the
DINH et al.: THERMORESISTIVE EFFECT FOR ADVANCED THERMAL SENSORS
following form [1], [2], [19]–[21]:
1
1
R = Aex p B
−
T
T0
969
(7)
where A is a constant; B is the thermal index, which is used to
evaluate the sensitivity of the thermoresistive effect in thermistors, as an alternative parameter to the TCR. B is calculated as
E g /2k for semiconductors in the intrinsic region and E d /k for
n-type semiconductors in the extrinsic region. The relationship
between B and TCR can be written as B = −T C R × T 2
[1], [2], [19]. In the following subsections, we discuss the
thermoresistive effect in several different materials for niche
applications.
1) Thermoresistive Effect in Silicon and Silicon Nanostructures: It is well-known that Si has been a main-stream
material for conventional thermal sensors such as thermal flow
sensors and convective accelerometers. The thermoresistive
effect in Si has been investigated in terms of temperature
dependence of resistivity, carrier concentration and carrier
mobility [22]–[30]. For example, the resistivity of in highly
doped silicon increases with increasing temperature, due to the
dominance of the scattering effect, and then decreases when
the temperature is high enough for providing thermal energy
to break silicon bonds and generating more carriers.
Recent research has focused on the physical effect of Si at
nano-scale levels since the carrier mobility of Si nanostructures
significantly depends their surface-area-to-volume ratio [31].
Great effort has been made for the development of silicon
nanowires (SiNWs) fabricated using bottom-up and top-down
approaches [32]–[34]. However, the thermoresistive sensitivity
of these SiNWs has been found to be similar to that of bulk
and micro-level silicon devices [35], [37], [38]. For example,
Wang et al. [35] reported a TCR of SiNWs fabricated by
a bottom-up vapor-liquid-solid (VLS) process, which ranges
from -3,700 to 120 ppm/K. As these TCR values are relatively
low and not of interest for thermal sensing applications,
achieving a higher thermoresistive sensitivity and the ability
to integrate into nano-systems would be a trend in the development of thermoresistive devices. We used a Focused Ion
Beam technique to fabricate SiNWs (Figure 3(a)) by locally
amorphizing the single crystal structure, then employed an
annealing process to recrystallize the structure for improving
the electrical conductivity [36] (Figure 3(b)). This top-down
process has resulted in a nanocrystalline structure for the
SiNWs (Figure 3); hence a high thermoresistive sensitivity of up to -12,000 ppm/K was observed for the SiNWs
(Figure 3(c,d)). However, the thermoresistive properties of
Si are significantly degraded at high temperatures. Therefore,
alternative materials such as silicon carbide have been investigated, and showed potential for thermal sensors operating in
harsh conditions. The following section will discuss the current
status of the thermoresistive effect in silicon carbide.
2) Thermoresistive Effect in Silicon Carbide (SiC) for
Thermal
Sensors
Operating
in
Harsh Environments: Silicon carbide (SiC) is one of the most promising candidates for thermal-based sensors operating in harsh
environments, due to its large band gap and superior physical properties [39]–[43]. The thermoresistive effect in SiC
Fig. 3. Thermoresistive effect in SiNWs. (a) A 10 μm×0.2 μm× 0.06 μm
SiNW fabricated by a Focused Ion Beam method. (b) Nanocyrstalline
structure of the SiNW examined by High-Resolution transmission electron
microscopy (HRTEM). (c) Relative resistance change of the SiNWs. (d) TCR
of the SiNWs. Reproduced from [34] and [36] with permission from the Royal
Society of Chemistry and Elsevier.
Fig. 4.
Thermoresistive effect in SiC. (a) Scanning electron
microscopy (SEM) image of the single crystalline 3C-SiC on a glass substrate
[48]. (b) TCR of 3C-SiC on glass [48]. (c) Relative resistance change and
TCR of a-SiC [54]. (d) Arrhenius plot of thermoresistance in a-SiC [54].
Reproduced from [48] and [54] with permission from the Royal Society of
Chemistry.
has been investigated in terms of the temperature effect
on carrier concentration and its mobility in crystalline SiC
[44]–[46]. In p-type 3C-SiC, the hole mobility is limited
by acoustic phonon scattering above 300 K and by ionized
impurity scattering at temperatures below 250 K [44], [45],
following the rule μ H ∼ T −β , where β value ranges from
1.2 to 1.4. In addition, highly doped n-type 3C-SiC has a
positive TCR from 400 to 7,200 ppm/K [47]. Up-to-date, most
of high quality 3C-SiC has been grown on Si substrate with
large area and low cost. However, a large current leakage to
the substrate was observed at temperatures above 100 ◦ C [48],
indicating that SiC on Si platform is not suitable for thermal
sensors at high temperatures. Therefore, SiC films have been
transferred on to a glass substrate [48] (Figure 4(a)) to avoid
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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 26, NO. 5, OCTOBER 2017
the current leakage. The thermoresistive properties of SiC on
glass has been investigated with a relatively high temperature coefficient of resistance of up to -5,500 ppm/K [48]
(Figure 4(b)). Another advantage of SiC is that its themoresistive properties are not affected by the visible light
illumination [49]. In addition, we proved that the thermoresistive effect can tune the sensitivity of SiC material to
stress/strain [50].
The hole mobility of other polytypes (6H-SiC and 4H-SiC)
was also investigated, and followed the same rule as that
of 3C-SiC, but with a stronger dependence on temperature,
in which the β value ranges from 2 to 2.6 [51], [52]. The
hypothetical reason is that the electron mobility of these
polytypes at high temperatures is restricted by intervalley scattering and acoustic phonon scattering. However, the mobility
of 3C-SiC is limited by acoustic phonon scattering, and little
affected by intervalley scattering, owing to the crystal symmetry of 3C-SiC. These scattering phenomena would affect
the temperature-dependent resistivity of n-type and p-type
6H-SiC. For example, Okojie et al. [53] reported a variation
of TCR from -3,400 to 5,600 ppm/K, which depends upon the
semiconductor type and the doping levels.
Recently, the thermoresistive effect in amorphous SiC
(a-SiC) has been investigated [54], showing a very large
negative TCR of from -16,000 to -4,000 ppm/K (Figure 4(c)).
By analyzing the themoresistive properties of a-SiC, the energy
characteristics of this system were investigated with two
activation thresholds of 150 and 205 meV, corresponding to
temperature ranges of 300 to 450 K and 450 to 580 K,
respectively (Figure 4(d)).
3) Thermoresistive Effect in Graphite for Low-Cost and
Environmentally Friendly Thermal Sensors: As discussed
in the previous sections, metals and semiconductors have
been employed for conventional thermal sensors. However,
these expensive materials have commonly involved complex
processes and toxic chemicals. Therefore, there is a strong
demand to investigate the low cost and environmentally
friendly materials for thermal sensors. Graphite is well-known
for this purpose because of its ubiquitousness and relatively
high temperature coefficient of resistance (TCR) [55]. The
TCR of graphite was observed to be positive [56], which
was explained based on the spacing of stacking faults in
graphite [57], tunneling conduction, impurity-assisted hopping
conduction and a combination of hopping and scattering of
carriers by phonons [56]. However, a number of other studies
indicated a negative TCR for different types of graphite, which
could be attributed to the defects and boundaries in graphite
[58]–[60]. A negative TCR of approximately -3000 ppm/K was
observed for temperatures of up to 200◦ C and a positive TCR
for higher temperatures [61]. Other studies have also reported
the thermoresistive effect in graphite at lower temperature
ranges [62], [63].
Alternatively, the thermoresistive effect in graphite inks
has been reported [64], [65], showing a positive TCR of
lower than 2200 ppm/K. However, pencil graphite showed a
relatively high negative resistance change from -2,900 to 4,400 ppm/K (Figure 5), which is comparable to that of common temperature sensing materials such as platinum, copper
Fig. 5. Thermoresistive effect in graphite [66]. (a) Graphite resistance change
as a function of temperature. (b) Temperature coefficient of resistance (TCR)
of pencil graphite. Reproduced from [66] with permission from the Royal
Society of Chemistry.
Fig. 6. Thermoresistive effect in carbon nanotubes [75]. (a) CNT resistance
change as a function of temperature. (b) Temperature coefficient of resistance (TCR) of CNT. Reproduced from Ref. [75] with permission from the
Royal Society of Chemistry.
and nickel [66]–[68], which was explained based on the theory
of the boundary between graphite crystallites (referred to
Figure 8(b), “C. Material choice and impact of morphologies”
section). In this theory, carriers are excited by thermal energy
can pass through or pass over the barrier between graphite
crystallites, which lead to an increase in the electrical conductivity of graphite.
4) Thermoresistive Effect in Carbon Based Nano-Materials:
Recent studies have paid attention to the thermoresistive effect
in nano-materials such as carbon nanotubes (CNTs) [69]–[72]
and graphene [73], [74]. However, thermoresistive sensitivities of these materials are relatively low (e.g. absolute TCR
values are commonly lower than 1250 ppm/K). In addition,
the current difficulties in releasing these materials make them
challenging to use in Joule heating based thermal sensors.
To date, few studies have demonstrated the use of these materials in Joule heating based thermoresistive sensors [75], [76].
Figure 6 shows the thermoresistive effect in CNT yarns with
a TCR of approximately 750 ppm/K, which has been used
for temperature and flow sensing applications [75]. In some
cases, when these materials are mixed with others to make a
composite (e.g. epoxy/MWCNT composite, multi-walled carbon nanotubes (MWCNTs)/styrene-b-(ethylene-co-butylene)b-styrene (SEBS) triblock copolymer), their thermoresistive
sensitivity can increase and they are potential candidates for
highly sensitive temperature sensors [20], [71], [72].
5) Thermoresistive Effect in Compounds and Other Materials: It is important to note that a giant thermoresistance
is desired for thermal sensing applications, and this can
be achieved using ceramics and nanocomposites. As such,
DINH et al.: THERMORESISTIVE EFFECT FOR ADVANCED THERMAL SENSORS
the giant thermoresistance with a temperature coefficient of
resistance of up to -6%/K (the thermal index B is from
2000 to 5000 K) was achieved [3], [77]. In the temperature
sensing area, it is well-known that ceramic thermistors have
been commercially available thanks to their high sensitivity
and accuracy and low cost [3]. In contrast to Si-based temperature sensors, oxide semiconductor (ceramic) thermistors
have a carrier concentration, which is solely determined by
the doping levels; however, the carrier mobility is thermally
activated with increasing temperature and the increase in the
conductivity is mainly due to hopping of carriers between
localized states in the mobility gap. This leads to an extremely
large thermoresistive effect in ceramic thermistors.
Different giant positive temperature coefficients of
resistance have been reported for various nano-composites
[78]–[83], in which the conduction mechanism is mainly
based on a volume expansion of the composites. This
leads to an increase of the distance between conductive nanotubes or nano-particles, or a breakage of conductive pathways.
Therefore, a positive temperature coefficient of resistance has
been commonly observed for the nano-composites. In some
cases, when the electrons in nano-composites are provided
enough thermal energy by the increasing temperature, they
can tunnel over the separating gaps and the conduction of the
composites is thermally activated with a negative TCR [78].
Recently, two-dimensional (2D) materials such as transition
metal dichalcogenides (e.g. MoS2 , MoSe2 and WS2 ) have
attracted much interest for electronics and sensors, owing to
their excellent mechanical, electronic, optoelectronic properties and potential for extremely low power consumption. These
materials are constructed based on the arrangement of atomic
layers. The electrical conductivity along c-axis (perpendicular
to the atomic layers), σ|| , is less than that perpendicular to
c-axis (σ⊥ ) and depends upon the number of layers [84]–[86].
When the number of layers decreases to a few (e.g. single layer
and bi-layer), the contribution of σ|| is significant. In this case,
it has been proven that the tunability of σ|| by electrical field
enables high-performance electronics (e.g. transistors) [87].
In addition, the tunability of σ|| by thermal energy (or temperature) can enhance thermoresistive properties of these materials.
However, the state-of-the-art results on thermoresistive effects
in 2D materials have been limited to bulk forms [84], [85]
and few layers at low temperature ranges (<300 K) [87].
Therefore, there are great opportunities to explore the potential
of 2D materials for thermoresistive sensors.
B. Thermoresistive Effect in Metals
In metals, electron concentration in metals is constant
(n = const) and contributes to electrical conductivity.
There are no more carriers generated as the temperature
increases, but the mobility of the existing carriers decreases
linearly (μe ∼ T −1 ), due to the scattering effect. As a result,
the resistivity or resistance R increases linearly with increasing
temperature (ρ ∼ T ) as follows:
R = R0 (1 + T C R(T − T0 ))
(8)
where R0 is the electrical resistance at reference temperature T0 . Therefore, metals commonly show a positive
971
temperature coefficient of resistance (TCR) [5], [15], [88].
Table I shows the TCR of several common metals, which
are commonly used for thermal sensing applications [5], [15].
The data from the I indicates positive TCR values ranging
from 4000 to 7000 ppm/K and a geometric effect of less than
30 ppm/K.
III. I MPACT OF D ESIGN AND P ROCESS ON P ERFORMANCE
OF T HERMORESISTORS
High-performance thermoresistors are needed to achieve
highly sensitive thermal sensors. For example, the sensitivity
of thermoresistors strongly depends on the substrates on which
these thermoresistors are fabricated. Moreover, doping type
and doping level play an important role in determining the
sensitivity of semiconducting thermoresistors. The dependence
of sensitivity is expanded to the morphology (e.g. crystalline,
polycrystalline and amorphous structures) of the thermoresistive materials. In addition, designers should also pay attention
to grain size of thermoresistors in choosing deposition temperature and thickness of thermoresistors.
A. Substrate Influence
For bulk materials, a substrate to support constructing thermoresistive devices is not commonly required. However, for
thin film thermoresistive sensors, there is an additional thermal
expansion mismatch between the films and their supporting
substrates. This effect of substrates on the thermoresistive
properties of thin films plays an important role in the accuracy
and sensitivity of such devices [14], [15], [90].
There are various studies, which have aimed at evaluating
the influence of the substrate on the thermoresistive property
of the thin films [14], [15], [90]–[92]. As such, Hall et al. [14]
suggested a contribution of 65 ppm/K for thin films supported
by glass substrates and a replacement for soft glass of fused
quartz can shift the TCR to 36 ppm/K. This effect is quite
significant, since the TCR of typical thin films is lower than
100 ppm/K. Similarly, Verma et al. [15], developed a general
equation for estimating the impact of thermal strain on the
thermoresistive effect in thin films as follows:
−2(αl f − αls ) γ (1 − μ f ) + μ f (1 − γ )
(9)
=
1 −μf
where is the difference between TCR of thin films with
and without substrates, αl f and αls are the thermal expansion
coefficient of films and substrates, respectively; μ f and γ are
the Poisson⣙s ratio of thin films and the strain coefficient
of resistivity (G F), respectively.
To date, very limited work is available on the impact
of semiconducting substrates on the thermoresistive properties [93]. On one hand, the current leakage to the semiconducting substrates at elevated temperatures would make the
semiconducting substrates not suitable candidates for thermoresistive sensors at high temperatures [93]. In addition,
it is required to isolate the thermoresistive sensing elements
from the heater and reduce the power loss to the substrate.
Therefore, the thermoresisisive sensors are commonly developed on suspended membranes or insulation substrates such as
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TABLE II
A CTIVATION /I ONIZATION E NERGY OF I MPURITIES IN S EMICONDUCTORS [98]–[110]
glass, alumina, fused quartz and silicon nitride [14], [94], [95].
In many cases, silicon dioxide (or glass) membranes are preferable as supporting layers for thermoresistive sensors because
silicon dioxide has a very low thermal conductivity (e.g. ∼
1.38 W/(mK)) in comparison with that of silicon nitride (e.g.
∼ 28 W/(mK)) [95]. This is due to the fact that a low thermal
conductivity would minimize the conduction heat loss to the
substrate.
On the other hand, a semiconducting substrate could be also
used as an active layer, and the combination of the substrate
and the functional layer can create other electronic devices
such as diodes [96]. The thermoresistive behavior between
these layers has been used for highly sensitive temperature
sensors. A detailed review on these devices can be found
elsewhere [97].
B. Doping Influence
1) Doping Type: As previously mentioned, the thermoresistive sensitivity depends upon the activation energy (or
ionization) energy of dopants. As such, a dopant with high
activation energy E d (or E a ) can provide a large temperature
coefficient of resistance (T C R = −E d /T 2 ) or a large slope
E d /k. The activation energy of donors or acceptors can be
calculated using band gap theory [2]. Nitrogen has been
commonly used as a donor for Si and SiC while aluminum (Al)
and boron (B) have been frequently employed as acceptors.
Table II shows the measured ionization energy (E d and E a )
for various impurities in Si and silicon carbide [98]–[110]
at room temperature. Doping in semiconductors refers to the
introduction a small amount of impurities into the crystal to
increase the number of carriers that are excited by thermal
energy and contribute to the electrical conductivity [1], [2].
In contrast, the doping in ceramics (a mixture of metal
dioxides) refers to the substitution of impurities into chemical
sites (e.g. metal or oxygen ions), which leads to changes
in the way electrons ’hop’ between ions of the chemical
species [3], [111], [112].
2) Doping Level: There are various studies on the doping
dependence of activation energy. It has been reported that
activation energy decreases with increasing doping levels [26],
[113]–[115]; hence there is a decrease in the thermoresistive
sensitivity. Lopatiuk-Tirpak et al. [113] reported a reduction of
activation energy of p-type ZnO from 212 to 135 meV with an
increase in the doping level from 1.3×1017 to 1.3×1018 cm −3 .
The dependence of this activation energy on doping levels is
attributed to the formation of the band-tail states, which extend
into the forbidden gap and the expansion of the acceptor band.
Fig. 7. Impact of doping levels on the thermoresistive effect in semiconductors. (a) Doping dependence of the thermoresistive effect in polysilicon [9].
Reprint with permission from [9]. (b) Doping dependence of the thermoresistive effect in silicon carbide [118].
It was also hypothesized that this dependence is due to the
Coulomb interaction between holes in the valence band (VB)
and the ionized acceptor states, which leads to the reduction
of binding energy. A similar behavior of Si-doped n-typed
GaN was reported, exhibiting a reduction of activation energy
from 28 to 21 meV with carrier concentrations increasing from
7.25×1017 to 1.6×1019 cm −3 [114]. An activation energy
of 40 to 54 meV was reported for SiC [116], also depending
on the doping level.
The thermoresistive sensitivity of other materials such as
silicon and silicon carbide can be controlled by adjusting
doping levels [9], [47], [53], [117]. Seto et al. [9] reported
a significant improvement in the thermoresistive sensitivity
of polysilicon with decreasing doping levels. At low doping
points (e.g. ∼ 1016 cm −3 ), the ionization energy is almost
half the energy gap value (approximately 0.5 eV) of single
crystalline silicon while it reduces to 0.025 eV at a high
doping level of 1019 cm −3 (Figure 7(a)). The mechanism of
this effect was hypothesized based on a decrease in the barrier
height and barrier width with increasing doping levels. The
TCR value of silicon was also reported to depend upon doping
levels [116]. As such, when decreasing the doping level from
1018 to 1014 cm −3 , the TCR value reduces from approximately
8000 ppm/K to almost 0 ppm/K at room temperature.
Furthermore, Shor et al. [47] have reported the doping
dependence of 3C-SiC resistivity. At unintentional doping
levels, all impurities are ionized below room temperature,
and the resistivity increases (T C R ∼ +0.72% /◦ C) with
increasing temperatures above room temperature due to the
dominant scattering effect. However, at low doping levels,
the temperature at which the resistivity reaches a minimum value, is higher (around 200 ◦ C). In the case of
degenerately doped 3C-SiC, all impurities are ionized at all
DINH et al.: THERMORESISTIVE EFFECT FOR ADVANCED THERMAL SENSORS
temperatures, and the scattering effect plays the dominant role,
leading to a constant TCR value of 400 ppm/K. Recently,
Latha et al. [118] has reported the effect of nitrogen doping
on the thermoresistive effect in 3C-SiC (Figure 7(b)), showing
an increase in the thermoresistive sensitivity with decreasing
doping levels of nitrogen. The change of 6H-SiC resistivity
depending on doping levels has been also investigated [53].
For instance, a low doping level (1017 cm −3 ) is fully ionized
at 0◦ C, while a high doping level (1019 cm −3 ) has a higher
ionization temperature of 500 ◦ C. At the same doping level
of 2 × 1019 cm −3 , the p-type 6H-SiC shows a higher absolute
TCR in comparison with the n-type. Also with high doping
levels, impurity scattering is considered to be the dominant
mechanism.
C. Material Choice and Impact of Morphologies
1) Material Choice: In general, the use of thermoresistive materials for developing thermal sensors depends upon
expected performance and applications. A large thermoresistive effect (i.e. large TCR) is desired for thermoresistive
sensors in terms of sensitivity. Nanocomposites and compound
materials (mentioned in Section II. A) are potential candidates
for this purpose; hence they are commonly employed as
sensitive temperature sensors [78]–[83]. However, the disadvantages of these materials are the non-linear and hysteresis characteristics, which require additional circuitry and
complex processing of sensor signals for accurate measurements. In addition, these materials have large resistivity; hence
they are not suitable for the thermal-based sensors such as
thermal flow sensors and convective inertial sensors which
involve heating elements. To increase the temperature of
the heating elements at low supply voltages, a low resistivity is required, which commonly lies between 10−1 to
10−6 cm [5]. Therefore, highly doped semiconductors (e.g.
highly doped single crystalline silicon with resistivity from
10−1 to 10−2 cm) and metals (e.g. platinum nickel with
resistivity is from 10−4 to 10−6 cm) are the conventional
candidates for these sensors. It is important to note that
semiconductors and metals are compatible with conventional
MEMS micro-machining technologies, which leads to the
commercialization of various thermal-based sensors employing these materials.
There is a strong demand to investigate alternative thermoresistive materials which can first satisfy the basic requirements: (1) high thermoresistive sensitivity, (2) low resistivity
and 3) compatibility with MEMS machining technologies. The
requirements for these alternative materials are also low cost,
ease of processing and ability to work in harsh environments
including high temperatures, high corrosion and high voltages.
Large band gap semiconductors such as silicon carbide are
promising candidates for thermal sensors operating in hostile environments thanks to corrosion inertness and superior
mechanical and electrical properties [39]–[43], [119], [120],
while carbon-based materials such as graphite are a good
choice for low cost and rapid prototyping of thermal
sensors [64]–[68].
2) Impact of Morphologies: There are three main morphologies of thermoresistive materials, namely single crystalline,
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Fig. 8. Transport mechanism in different morphologies. (a) Single crystalline.
(b) Polycrystalline.
polycrystalline and amorphous configurations. Among these,
single crystalline and polycrystalline materials can achieve
a reasonable low resistivity (e.g. 0.1 cm for silicon) for
heating purposes in various thermal-based sensors such as
thermal flow sensors and convective accelerometers. In pure
crystalline materials, the generation of carrier concentration
and the increase in carrier mobility with increasing temperature play an important role in the behavior of the thermoresistive effect (Figure 8(a)) [1], [2]. For example, in highly
doped single crystalline silicon, all impurities are ionized at
room temperature, and only scattering is considered at higher
temperatures, which leads to a positive temperature coefficient
of resistance (e.g. normally lower than 5,000 ppm/K).
However, a polycrystalline material is a complex composition of crystallites and the boundaries between them [9],
[121], [122]. Therefore, some models have been proposed
to explain the resistivity dependence on polycrystalline morphology. As such, Seto [9] hypothesized that boundaries in
polycrystalline material can trap carriers, creating a potential
barrier φ to impede the movement of carriers through the
barrier. Therefore, the boundary resistance plays an dominant
role in the thermoresistive effect of polycrystalline material.
The boundaries are sensitive to temperature change as both
tunnelling and thermionic emission mechanisms can contribute
to a decrease in electrical resistance with increasing temperature (Figure 8(b)). When the polycrystalline material is doped
at high levels, the barrier is low; hence the thermionic emission
mechanism is dominant. The thermoresistive sensitivity was
observed to be low in highly doped polycrystalline silicon.
The model proposed by Seto [9] has been used to explain the
high thermosensitivity of various polycrystalline materials [9],
[121], [122]. The temperature-dependent electrical resistance
R of poly/nano crystalline structures can be determined by the
following equation:
φ
(10)
R = Aex p
kT
where k is the Boltzmann constant, R is the electrical resistance at temperature T , and A is a constant.
In polycrystalline metals, the grain boundary plays a
dominant role when the grain size is very small (e.g.
much smaller than the electron mean free path) [15].
In this case, the TCR of metal thin films can be much less
than the bulk value and it could turn to a negative value if
the TCR of bulk material is less than temperature coefficient
of bulk mean free path [15], [92]. In ceramics, the role
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of grain boundaries on the thermoresistive properties is still
controversial [123]–[125]. As such, it has been reported that
the thermoresistive sensitivity of grain boundaries is much
higher than that of bulk materials and more sensitive to
annealing conditions [123]. However, some other reports have
shown that the activation energy of grain boundaries is the
same as that of bulk boundaries [124], [125].
Another important morphology of semiconductors is amorphous, which is known for its localized and extended states.
Amorphous semiconductors have an energy level between
them, named mobility edge. The extended and localized states
have a different density of state (DOS), which can be a constant, parabolic or exponent function of temperature depending
on the temperature range. In a broad range of temperature
T , the conductivity σ of amorphous semiconductors can be
expressed in the form:
β
Ea
(11)
σ = σ0 ex p −
kT
where σ0 is the pre-exponential factor, and the power
exponent β depends on temperature range. E a denotes
the activation energy and k is the Boltzmann constant.
Mott et al. [126] developed the concept of variable-range
hopping (VRH) for the temperature-dependent conductivity
with the assumption of a constant DOS function. The value of
β in Eq. 11 was found to be 1/4 for the VRH regime. However,
due to the interactions between localized electrons, a Coulomb
gap exists in the DOS, which has a parabolic distribution at
low temperatures. As a result, β = 1/2 shows the presence
of the Coulomb gap [127]. At temperatures high enough (e.g.
temperatures close to room temperature), the transport energy
moves upward towards the mobility edge. Electron transitions
between the de-localized states above the mobility edge and
the localized band tail mainly contribute to the conduction
of amorphous semiconductors [127]. The temperature dependence of conductivity is observed with β = 1, showing an
activation of electrons over the mobility edge [128]. This
mechanism has been used for investigating the thermoresistive
effect in a-Si and a-Si:H, with TCR values ranging from 20,000 ppm/K to -80,000 ppm/K for a temperature range
of 300 to 350 K [129]–[131].
D. Deposition Temperature, Grain Size and Thickness
In general, when deposition temperatures (or substrate
temperatures) increase, the grain size of thermoresistor films
increases and the resistivity decreases. This could tune the
thermoresistive sensitivity of the films [10], [132], [133]. For
example, it has been reported that an increase in the deposition
temperature from 25 to 300 ◦ C can change the TCR of CuNi
thin film resistors from negative (-50 ppm/K) to zero and
then positive (80 ppm/K) [10]. This could be attributed to
the enhancement of amorphization under lower-temperature
depositions. It has been found that the crystallinity of the
films degrades significantly when the substrate temperature
decreases [10], [132]. For instance, Himanshu et al. [134]
reported that improvement in crystallinity could be achieved
when the deposition temperature increases from 350 to 850 ◦ C;
Fig. 9. Influence of substrate temperature on the thermoresistive effect in
SiC thin films [134].
Fig. 10. The dependence of thermoresistive effect on thickness of films.
(a) Thickness dependence of TCR in platinum [136]. Reprint with permission
from [136]. (b) Thickness dependence of TCR in silicon carbide [17].
however, the thermoresistive sensitivity also decreases with a
decrease in activation energy from 0.57 to 0.086 eV (Figure 9).
In addition, the thermoresistive effect in polycrystalline
metal films has been theoretically investigated [15], [91], [92],
[135], indicating a dependence of TCR on grain size diameter.
As such, the TCR can be small and negative for films with a
very small grain size, but it could approach a large positive
value (similar to the TCR of bulk material) by using a very
large grain size [92].
It has been reported that the thermoresistive sensitivity
depends upon the thickness of thin films. For example, the thermoresistivity of platinum nano thin films is lower than that
of bulk materials [136]–[138] (Figure 10(a)). However, for
semiconductor thin films such as SiC, it has been proven that
the thinner the film thickness, the higher the thermoresistive
sensitivity (or the higher the TCR) [17], [139]. This phenomenon has been explained based on the free carrier trapping
model [140], [141]. As such, thinner films normally have
a smaller grain size and have more defects and boundaries,
which make a potential barrier to impede the movement of
free carriers. Both thermionic and tunnelling currents passing
this barrier contribute to the thermosensitivity of the ultrathin films. Figure 10(b) shows the thickness dependence
of the TCR of SiC thin films, and indicates a TCR of
from -1400 ppm/K to 2200 ppm/K for the film thickness
of 16963 to 1530 A, respectively [17].
DINH et al.: THERMORESISTIVE EFFECT FOR ADVANCED THERMAL SENSORS
IV. D ESIRABLE F EATURES FOR T HERMAL S ENSORS
For effectively realizing the thermoresistive effect for the
applications of thermal sensors such as temperature sensors,
thermal flow sensors, convective accelerometers and gyroscopes, several important features need to be considered in the
design and implementation of thermal-based sensors. These
are thermoresistive sensitivity, linearity of response, thermal
time response and other features.
A. Sensitivity
Among the desirable parameters for thermal sensors, sensitivity is one of the most important features because it represents the efficiency of detection or monitoring. As previously
mentioned, the temperature coefficient of resistance (TCR)
has been commonly used for evaluating the sensitivity of the
thermoresistive effect, defined by relative resistance change to
the temperature variation. The units of TCR, often found in
literature, includes ppm/K (parts-per million per Kelvin) and
%/◦ C (percent per Celsius). Moreover, for temperature sensors
using ceramic and semiconductor materials, the thermal index
B (K), which commonly lies between 1,000 K and 10,000 K,
has also been employed as a sensitivity parameter.
In addition, giant thermoresistive effect is desired for temperature sensors; hence a ceramic material or a composite/mixture is often deployed since these materials can provide
an extremely high TCR of up to 1012 ppm/K [82]. However,
these materials might not be suitable for other thermal sensors
based on the Joule heating effect, such as thermal flow sensors
and inertial sensors. This is due to the fact that these sensors
require a low resistivity to reduce the voltage or current supply
for heating. Therefore, metals and highly doped semiconductors have been commonly employed to fabricate this type
of sensors. However, these materials have some drawbacks
in terms of low thermoresistive sensitivity (e.g. lower than
5,000 ppm/K).
It is important to note that detecting temperature changes in
thermal-based sensors which operate based on Joule heating
is quite challenging, since these sensors employ materials
with low thermoresistive sensitivity. Therefore, the resistance
changes (R/R) in these sensors are commonly converted to
a voltage change (V ) by using a Wheatstone bridge, and this
voltage change can be amplified using signal amplifiers.
Alternatively, a thermoresistive insensitivity or a zero temperature coefficient of resistance (TCR) is desired for the
precise control of temperature in heaters and other sensing applications including strain and pressure measurements.
Many studies have focused on developing zero-TCR systems
with semiconductors and inorganic compounds [117], [118],
[140], [142], [143]. For example, controlling doping levels has
been proven to be an effective approach to achieve zero-TCR,
which is commonly done in the in situ growth process of the
semiconductor films [117], [118], [140]. However, a common
strategy for achieving zero-TCR in polymers/composites is to
mix a negative-TCR material with a positive-TCR material.
For example, Chu et al. [142], [143] reported a near zero-TCR
of conductive composites consisting of a bi-layer of negative
TCR carbon nanotube and positive TCR carbon black, showing
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less than 2% variation of relative resistance change when the
temperature reaches 200 ◦ C. In some cases, the effect of the
substrates on the thin films is significant as it can tune the
TCR from a negative [66] value to a positive value [144].
B. Linearity
Linearity is another desirable parameter for thermal-based
sensors, since it is responsible for the accuracy of measurement. Thermal sensors with linear characteristics have
various benefits, not only in the accuracy of measurement,
but also in terms of simplicity in the design of circuitry and
implementation.
Most metals show excellent linearity in a wide range of
temperatures; hence they have been commonly deployed for
fabricating thermal flow sensors, convective accelerometers
and gyroscopes. The reason for the linear characteristics of
metals is that the number of electrons in metals is constant, while electron mobility is inversely proportional to
temperature; hence using equation 5, the resistivity is linearly
dependent on temperature.
However, the resistance of semiconductors is exponentially
dependent on temperature as shown in Eq. 7. Therefore,
to realize the design of circuitry and the measurement of
signals, Eq. 7 is usually converted to the following form,
which presents the linear relationship between ln(R/R0 ) (R
and R0 are the electrical resistance at temperature T and T0 ,
respectively) and 1/T :
1
(12)
ln (R/R0 ) = A − B
T
where A = B/T0 is a constant. Equation 12 has been
commonly used for representing the Arrhenius law. From
plotting Eq. 12, the sensitivity of the thermoresistive effect
B or the activation energy E a = B × k, where k is the
Boltzmann constant, can be determined. For example, Figure 7
shows the linear relationship between ln(ρ/ρ0 ) and 1/kT ,
indicating an activation energy of 0.025 eV to half energy
gap of single crystalline silicon. It should be noted that
highly doped semiconductors could also achieve a linearity
between electrical resistance and temperature, since all impurities have the potential to be ionized at room temperature and
the resistance depends upon the scattering mechanism with
changing temperature [49]. This behaviour of highly doped
semiconductors is similar to that of metals. Therefore, using
high doping levels for the Joule heating based sensors could
achieve a linear characteristic [16].
C. Thermal Time Response
Apart from the sensitivity and the linearity, thermal time
response is also considered as a key feature for thermal
sensors, as it presents the capability to respond instantaneously
to the change in external signals such as temperature, flow
and acceleration. Theoretically, the thermal time response of
thermoresistive sensors is limited by the thermal time constant
τ = Rt h × Ct h , where Rt h and Ct h are the thermal resistance and thermal capacitance of the sensor [145]. Thermal
resistance can be calculated as Rt h = L/(A × k), where
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Fig. 11. Response time of thermal flow sensors. (a) The 63.2% response
time of a sensor. (b) A thermal time response of 2.5 ms is determined from
fitting the equation T = A − B × ex p(−t/τ ) [149]. Reprint with permission
from [149].
L, A and k are the length, cross-sectional area and thermal
conductivity of the sensor material, respectively. A material
with a higher thermal conductivity offers a lower thermal
resistance; hence it has a faster thermal time response. For
example, 4H-SiC would be preferable to Si for developing
thermal sensors with fast thermal time responses because the
thermal conductivity of 4H-SiC is much higher than that of
Si [146]. Thermal capacitance can be approximated as Ct h =
ρt h × V × C H , where ρt h , V and C H are the density, volume
and heat capacity of the sensor, respectively. The density of
some metals such as platinum (ρt h =21.45 g/cm3 ) is larger
than that of semiconductors such as silicon (ρt h =2.33 g/cm3 )
and silicon carbide (ρt h =3.2 g/cm3 ). However, platinum has
a much lower heat capacity (C H =125 J/(kgK)) in comparison
to silicon (C H =700 J/(kgK)). Therefore, a common strategy
to achieve a fast thermal time response is to scale down the
thermoresistive elements or choose materials with high thermal
conductivity, low density and low heat capability. As such,
nano structures (e.g. nanowires and nanobelts) would offer
fast time responses which are useful for measuring systems
with rapid changes of temperature.
Experimentally, the thermal response time is commonly
defined as the time needed for the amplitude of the output
signal to reach approximately 63.2 % or 90 % of that of a
steady-state signal, due to a change of external parameters
[94], [147], [148]. Figure 11(a) shows the response time of a
thermal flow sensor, which is determined by 63.2 % amplitude
of the steady-state signal [147]. The thermal response time
could also be determined from the exponential fit for the time
dependence of temperature response T = A − B ×ex p(−t/τ ),
where A and B are constants; t and τ are the time parameter
and the thermal time response, respectively [149]. Figure 11(b)
shows the response time of τ =2.5 ms by fitting the response of
the sensor [149]. For various MEMS thermal sensors reported
in the literature [94], [147]–[149], the thermal response time
is within the ms range, corresponding to a the bandwidth of
the kHz range. These responses satisfy the practical applications such as measuring human respiration, which requires the
monitoring of 12 to 20 breaths per minute, corresponding to
a bandwidth of only 0.2 to 0.33 Hz.
advantages of micro and nanomachining technologies. For
example, a small-in-size heater in thermal flow sensors could
be heated up to a high temperature with low power because of
its small volume, which can also lead to a faster response of
the sensor. For example, Cubukcu et. al. [150] has proven that
the sensitivity of the sensor at a constant power consumption is
improved by scaling down the size of its structures. Therefore,
nanostructures such as nanowires and 2D materials are of
interest in terms of low power consumption and fast thermal
response.
For thermal sensors not requiring a heating element such
as temperature sensors, a small size (e.g. length, width and
thickness) is of interest as it leads to a faster response to temperature change and a more uniform temperature distribution
within the sensor [75]. It is expected that when the size of the
thermal sensor is scaled down to lower than a certain value
(e.g. 100 nm), the thermoresisitive sensitivity could decrease
due to the impact of material morphologies at nanoscales
[136]–[138]. However, for thermal flow sensors and inertial
sensors which require heaters and thermoresistive sensing elements, a longer (up to 1000 μm) and wider (up to 70 μm) heating elements can result in a larger output signal from the sensor
due to the reduced heat conduction to the substrate [149].
However, a long heating element leads to a higher resistance
which requires a higher supply voltage. In addition, a wider
heating element offers a slower time response. The distance
between heating and sensing elements is another important
geometrical parameter which can have an even greater effect
on the sensitivity and measurement range than the size of the
sensor [151]. In some cases, T-shape sensing elements (with
two ends free to expand or contract when the temperature
changes) can be utilized for lowering the thermally induced
stress [152], [153].
With regards to design, themoresistive sensors fabricated
on suspending isolation substrates could reduce power loss in
comparison to sensors located on thick substrates or semiconducting substrates. To realize the suspended structures,
electrodes and thermoresistive elements are commonly patterned first using conventional lithography and surface etching
processes; then wet etching of bulk substrates (e.g. silicon) is
performed from frontside or backside to release the membrane
structures [94], [151].
A number of the thermal flow sensors could operate under
sub-mW power consumption (lower than 1 mW) using suspending isolation structures, while these devices can maintain
a large measurement range with high resolution and without
loosing its fast time response [154], [155]. It is also important
to note that a decrease in the supply power leads to a lower
sensitivity of such sensors. Therefore, a large thermoresistive
effect is desired to achieve a high sensitivity and high resolution of detection at low power consumption [150].
E. Stability and Other Desirable Features
D. Low Power Consumption
Low power consumption is an obviously desirable feature for not only thermal sensors but also other electronic
devices. This can be achieved through miniaturization, taking
For practical applications, the repeatability, long-term
stability and ability to work in harsh environments without degradation of performance are also desirable features for thermoresistive sensors. Among these features, the
DINH et al.: THERMORESISTIVE EFFECT FOR ADVANCED THERMAL SENSORS
repeatability and stability are essential for the reliability and
accuracy of measurements. These desired characteristics are
commonly determined from repeated cycle tests. For example,
Shingo Harada et al. [156] observed the consistence of the
performance of a flexible thermoresistive temperature sensor
after several repeated cycle tests at both the room temperature
and an elevated temperature. Thermoresistive structures are
typically placed outdoors where the temperature variation,
humidity and chemical species are not controlled. This leads
to the drift or instability of the sensor signal. For example, when a ceramic thermoresistive element is exposed to
atmospheric conditions, its surface chemically adsorbs and
dissociates water vapor molecules to form layers of hydroxyl
ions, followed by a physical absorption. This results in a
change in the electrical conductivity of the themoresistive
element [157]. Low porousity thermoresistive materials are
desirable for minimizing the impact of humidity on the resistive structures [3], [157]. A signal processing method has been
proposed to possibly eliminate the effect of humidity and other
factors [158].
In addition, various metals (e.g. aluminum) and semiconductors (e.g. silicon) cannot operate in harsh conditions such
as high temperatures. This leads to a strong demand for
developing alternative thermoresistive materials, which are
able to work in harsh environments. Wide band gap semiconductors have been recently studied with an aim towards high
temperature applications, due to their superior electrical and
mechanical properties at high temperatures. For example, silicon carbide has demonstrated excellent stability when exposed
to 400 ◦ C in air for 2000 hours [159].
V. A PPLICATIONS OF T HERMORESISTIVE E FFECT
The insight into the thermoresistive effect described in the
previous sections has led to various successful MEMS sensor
applications. Among them, thermal flow sensors have been
mainly developed using metals (e.g. platinum, gold and nickel)
and semiconductors (e.g. silicon and polysilicon). The good
conductivity of these materials is required to measure the
temperature of the thermoresistors at a low voltage supply. The
resistance change of the thermoresistors induced by a flow or a
temperature change around the sensor is used to determine
characteristics of the flow. Another application of the thermoresistive effect is the detection of acceleration. However,
convective accelerometers, commonly employing metals and
semiconductors, work based on the movement of the bubbles
of heated fluid around them, which leads to an asymmetry
of the temperature profile. Therefore, these accelerometers
require an enclosed chamber and thermoresistors around them
to detect the change of temperature profile.
In addition, one of the most important applications of
the thermoresistive effect is temperature sensing. Temperature
change directly leads to the change in the electrical resistance
of thermoresistive materials. A number of materials have been
deployed for this purpose, namely metals, semiconductors,
nanomaterials and other compounds/mixtures. Temperature
sensors could be employed for a wide range of materials
because these sensors do not require high conductivity like
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thermal flow sensors and convective accelerometers which
work based on the Joule heating effect. This section will discuss in details the current status of development of thermoresistive sensors such as temperature sensors, thermoresistive
flow sensors, convective accelerometers and other advanced
thermal sensors based on the thermoresistive effect.
A. Temperature Sensors
In general, thermocouples, and metal and ceramic thermistors are commonly used as temperature sensors, and are
commercially available [3]. Ceramic thermistors, a type of
NTCR temperature sensors, have shown various important
advantages in terms of high sensitivity, signal-to noise ratios,
small size and low cost. The sensitivity of these temperature
sensors depends upon the grain size and the composition of the
metallic oxides [3]. However, complexity in terms of the chemical composition, the formation of micro-structures and the
oxidation processes has led to various difficulties in controlling
the processing parameters and the chemical homogeneity. As a
result, the process for achieving highly stable and reproducible
ceramic thermistors is a significant challenge; hence, costs are
raised, limiting their specific applications.
The aforementioned difficulties with the ceramic thermistors have resulted in a strong demand to develop simple and single-film semiconductor thermistors, which are
stable and reproducible, and avoid the use of chemical
mixes [159]–[164]. Efforts have been made to improve these
characteristics. For example, SiC thermistors have been developed thanks to their ability to work in harsh environments (e.g.
high temperature range) [161]–[164]. The main advantage of
SiC thermistors is the fast thermal response and the ability
to operate at high temperatures without degrading stability
and reproducibility [159]–[164]. In addition, Wasa et al. [159]
developed a highly reliable SiC thermistor with no significant
ageing after 2000 hours exposed to air at 400 ◦ C. This SiC
thermistor was also tested with 10000 cycles at a temperature
change rate of 75 ◦ C/second. In comparison to the silicon
counterpart, SiC thermistors with their excellent stability under
the impacts of the environments such as humidity and erosion,
have made them an attractive candidate for temperature sensing in harsh environments [159]–[164].
Metal thermistors have also been developed thanks to their
highly linear response to temperature change; hence, they are
simple in circuit design and signal measurement [5], [13].
However, relatively low sensitivity limits their applications. In contrast, composite mixture-based thermistors show
extremely high sensitivity, which can be several orders larger
than that of the ceramic and semiconductor thermistors.
These thermistors could be used for human body temperature detection, owing to their flexibility, stretchability and
wearability. However, the material cost and the narrow working temperature range are the main disadvantages of these
thermistors [81], [82]. The performance and characteristics of
the temperature sensors are summarized in Table III.
B. Thermal Flow Sensors
Thermal flow sensors (i.e. flow sensors which measure
the velocity of surrounding fluids and the direction of fluid
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TABLE III
C HARACTERISTICS OF T EMPERATURE S ENSORS
Fig. 12. Operational concept of thermal sensors and circuitry for measurement of flow signals [175]. (a) Hot-wire/hot-film principle. (b) Calorimetric principle.
(c) Time of flight concept.
movement) operate based on heat transfer from a heater
to the environment [165]. Sensitive thermoresistive elements
are commonly employed for the detection of temperature
changes, which come from the velocity or direction change
of fluids. The working principles of three common thermal
flow sensors (e.g. hot-wire/hot-film, calorimetric and time
of flight) are shown in Figure 12. The working principle,
fabrication and performance of various thermal flow sensors
have been extensively reviewed [4], [5]. Table IV summarizes
the performance of various thermal flow sensors reported in
literature.
1) Hot-Wire and Hot-Film Flow Sensors: In hot-wire and
hot-film configurations, a wire/film acts as both a heater and
a sensor. The temperature is raised to a steady state via Joule
heating and will remain that way until a flow is applied.
The cooling effect from the flow reduces the temperature and
hence changes the resistance of the heater (Figure 12(a)). This
resistance change is usually converted into a voltage change
using a Wheatstone bridge [8], [166]–[169]. The equation
governing the working principle of hot-wire and hot-film
thermal flow sensors is an energy balance between Joule
heating and convective cooling as follows:
R I 2 = h A (T − Te )
overall boundary area of the heater with the surrounding
environment.
The thermoresistive effect in metals (e.g. platinum)
and semiconductors (e.g. polysilicon) has been commonly
employed for developing sensitive thermal flow sensors, since
these materials offer high thermoresistivity (high TCRs) and
proper resistivity for heating and sensing [8], [11], [169].
For example, platinum has been deployed to fabricate hotfilm flow sensors for measuring air velocity, which showed
a high sensitivity of 0.177 mV(m/s)−1/2/mW at a power
consumption of 45.1 mW [11]. However, these sensors have
some drawbacks in terms of working in harsh environments
(e.g. high temperatures and corrosion) due to the degradation
of the sensor materials. Therefore, wide band gap semiconductors such as SiC have also been used to develop hot-wire/hotfilm flow sensors. For example, Lyons et al. [149] developed
a hot wire bridge thermal flow sensor using 3C-SiC grown
on a Si substrate, in which two bridges were fabricated as a
heater and a temperature sensor, and arranged in a Wheatstone
bridge with two external resistors. The flow sensor showed
a fast thermal time response of 3 ms, high sensitivity, high
mechanical strength and a good ability to be heated to high
temperatures due to the high melting point of SiC.
(13)
where R, I , T and Te are the resistance of the heater, supply
current, temperature of heater and temperature of environment,
respectively; h is the heat transfer coefficient and A is the
2) Calorimetric Flow Sensors: Another thermal flow mechanism is calorimetric sensing, which uses the asymmetry of
temperature profiles of upstream and downstream temperature
sensors when flow is applied (Figure 12(b)). The temperature
DINH et al.: THERMORESISTIVE EFFECT FOR ADVANCED THERMAL SENSORS
979
TABLE IV
C HARACTERISTICS OF T HERMAL F LOW S ENSORS
difference T between the upstream and downstream sensing
elements can be defined in the form:
T = T e x1 d1 − e x2 d2
(14)
where T is the heater temperature; d1 and d2 are distances
from the heater to the upstream and downstream resistors.
Parameters x 1 and x 2 depend on the surrounding fluid velocity,
thermal diffusivity of the fluid and boundary layer thickness.
This sensing method is preferable to hot wire and hot film
techniques because it is sensitive to small flows and able to
detect flow direction due to the presence of the upstream
and downstream temperature sensors. In calorimetric sensing, metals and semiconductors have also been commonly
used. As such, Cubukcu et al. [150] developed a germanium calorimetric thermal flow sensor with a high sensitivity
of 232.77 V/W/(m/s), a fast thermal response of 10 ms and a
low power consumption (less than 6 mW). In addition, great
effort has been paid to develop calorimetric flow sensors for
high-temperature environments using SiC [139]. Lee et al. successfully fabricated a n-poly SiC resistive heater surrounded
by one downstream and two upstream temperature sensors on
silicon nitride and silicon substrates [173]. This sensor has a
sensitivity of 0.73 /sccm and a negative TCR of 1240 ppm/K
for both heater and temperature sensors.
3) Time-of-Flight Flow Sensors: In the time of flight thermal sensing method, flow information is tracked by measuring
the transition time of a thermal pulse between a heater and
a temperature sensor (Figure 12(c)). The transition time is
determined based on the flow velocity, thermal conductivity
and diffusivity of the fluid [4], [5].
C. Convective Inertial Sensors
1) Convective Accelerometers: The most common mechanical accelerometers utilize a suspended proof mass, which
generates displacement with applied accelerations; hence it
induces stress/strain that can be measured using piezoresistive
elements. However, mechanical accelerometers have some
drawbacks such as low shock resistance and a complex fabrication process. Therefore, convective accelerometers without
any proof mass have been developed to avoid these drawbacks.
The working principle of convective accelerometers was proposed by Weber [176], and then implemented using MEMS
technology by Leung et al. [177].
The development of convective accelerometers is based on
single-axis (1-D), two-axes (2D) and three-axes (3D) configurations. The working principle of convective accelerometers
is shown in Fig. 13(a). Convective accelerometers operate on
the movement of a hot bubble of fluid around a heater (a
self-heated resistive element by Joule heating), caused by
external accelerations. The inertial force, when applied to the
mass of the hot bubble, causes asymmetry of the temperature
profile around the heater (Figure 13(a)). This temperature
difference is detected using two thermoresistive temperature
sensors, which are arranged at equal distances from the heater.
Convective accelerometers are required for packaging in a hermetic/enclosed chamber to prevent disturbance from external
environments. These sensors commonly employ a cavity to
thermally insulate the heater from the substrate. This helps
lower the power consumption of accelerometers.
In the last 20 years, there have been a number of reports on
the development of convective accelerometers towards high
980
Fig. 13.
JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 26, NO. 5, OCTOBER 2017
Convective inertial sensors. (a) Working principle of convective accelerometers [182]. (b) Working principle of thermal gyroscopes [16].
TABLE V
T HE P ERFORMANCE OF I NERTIAL S ENSORS
sensitivity, fast response and multi-direction detection [6],
[12], [152], [153], [176]–[180], [180], [181], [183]–[185]. The
performance of various convective accelerometers is summarized in Table V.
As high sensitivity is desired for convective accelerometers, the optimization of the design parameters has been
intensively investigated. The optimization results reported by
Luo et al. [179]–[181] show that an increase in the supply power and cavity sizes can enhance the sensitivity of
convective accelerometers. However, the frequency response
decreases with increasing cavity size. Surrounding environments with a low viscosity and high thermal diffusivity also
contribute to the high sensitivity and fast frequency response of
thermal accelerometers. For example Bahari et al. [6] reported
that a sensitivity improvement of more than 400 times could
be made by changing the filled candidate gases from N2
to C4 H8 .
To enable the functionality of multi-direction detection,
planar convective accelerometers (2D) have been developed on
a plane or thin film, which can be simply fabricated using standard MEMS technologies. However, 3D accelerometers, which
are capable of measuring out-of-plane acceleration, have been
significantly challenging to fabricate with a requirement of
various complex and nonstandard techniques [7]. To date, only
Nguyen et al. [12] have reported a monolithic 3-axis thermal
convective accelerometer based on the working principle of
DINH et al.: THERMORESISTIVE EFFECT FOR ADVANCED THERMAL SENSORS
planar accelerometers. However, the z-axis sensitivity of this
sensor is relatively low, and it also requires complex additional
circuitry for signal processing.
2) Convective Gyroscopes: It is well known that microgyroscopes find applications in the automotive industry such
as in anti-skid and stability control (e.g. camera and cell phone
stabilization), and anti-roll applications. Gyroscopes can also
been found in inertial mouses and displays and other electronic
devices. Common mechanical gyroscopes use a proof mass
supported by springs as a strain-induced structure, and operate
based on the Coriolis effect.
As conventional gyroscopes employ moving parts, they
are potentially fragile, and have low shock resistance and
high levels of vibration noise. Therefore, thermal convective
gyroscopes have been proposed by Van et al. [186]
(Figure 13(b)). The authors proposed a dual-axis convective
micro-gyroscope with high resolution of 0.05 deg/s, high
sensitivity of 0.1mV/deg/s and bandwidth of 60 Hz at
-3 dB. Since then, there have been a number of reports
on the development of convective gyroscopes offering low
power-consumption, high sensitivity and multi-direction
detection (e.g. three-dimension convective gyroscopes)
[16], [186]–[190]. Table V summarizes the recent advances
in convective gyroscopes.
D. Other Thermoresistive Sensors
The thermoresistive effect has been also utilized for chemical composition sensing applications including gas sensors
[191]–[194]. For example, in combustion a thermoresistive
element can detect the exposure of gases on its active surface, due to the heat rise of combustion [192], [194]. Metal
oxides and their compounds are often used for this application because they offer good catalytic properties. Platinum,
palladium, and thoria compounds are also excellent catalysts
for combustion application. In addition, thermoresistors have
been also deployed for the measurement of gas humidity [195].
Furthermore, thermistors which can work in low temperature
environments have been used as temperature sensors to detect
cryogenic liquid level [196], [197]. Finally, thermoresistors,
used as a Pirani gauge heated by a Joule heating current, have
been commonly employed for monitoring low pressure ranging
from 0.5 to 10−4 torr [198], [199].
VI. C ONCLUSION AND P ERSPECTIVES
In the past few decades, the thermoresistive effect in
metals and semiconductors has been intensively investigated.
The thermoresistive sensitivity of metals has been found to
commonly lie between 3,000 to 7,000 ppm/K, while that
of silicon ranges from -25,000 ppm/K to 10,000 ppm/K.
Giant thermoresistive sensitivity in ceramics and other compounds/mixtures, which can reach up to 1012 ppm/K, has
also been achieved. Moreover, the thermoresistive effect in
wide band gap semiconductors such as silicon carbide has
been examined, showing their potential for operating in high
temperature environments. 3C-SiC (β − Si C) and 6H-SiC
(α − Si C) have been investigated for their thermoresistive
effects, indicating their strong feasibility for thermal sensors.
981
However, lowering the bulk wafer cost of (α−Si C), and growing (β − Si C) thin films in a large area are both necessary for
the implementation of thermal sensors. Furthermore, impacts
of growth and fabrication parameters on the thermoresistive
sensitivity of silicon carbide polytypes would be examined.
These parameters include, but not limited to doping levels,
thickness of SiC films and type of substrates.
The electrical resistivity of single crystalline SiC is potentially useful for sensors employing Joule heating effect.
As such, this material can be employed for developing thermal
flow sensors and convective accelerometers, which operate in
high temperature environments. Thanks to its superior thermal
characteristics such as high melting point, SiC could be used
in local heaters integrated within SiC systems to heat other
structures up to high temperatures, which eliminates the use
of external heaters. In addition, SiC grown on Si and subsequently transferred onto glass by Focused Ion Beam (FIB) can
avoid current leakage through the SiC/Si junction. However,
for large scale production, a bonding technique is recommended to transfer a large-area of SiC on to glass. Therefore,
SiC bonded on glass would be a suitable platform for low-cost
thermal sensors operating in high-temperature environments.
Recently, significant progress has been made in the fabrication and characterization of MEMS thermal sensors, which utilize the thermoresistive effect in many metals such as platinum
and semiconductors including silicon and polysilicon. These
sensors have shown high sensitivity, linear response and low
power consumption, which has led to their commercialization.
However, the high cost and the low capability to work in
high temperature environments are the current drawbacks.
Significant development of high-temperature thermal sensors
is expected to be made in the near future, employing large band
gap semiconductors such as silicon carbide. While a number
of power electronics and circuits have been commercialized,
the need for the integration of electronic circuits with thermal
sensors, allowing operation at high temperatures, is expected to
lead to even more development of high-temperature sensors.
For this purpose, alternative thermal sensing materials with
their high thermoresistive sensitivity need to be investigated.
It is also important to develop proper packaging for thermal
sensors because thermal expansion at high temperatures can
cause cracking in devices.
In addition, the development of thermal sensors could be
driven towards miniaturization, a wide range of measurement without signal saturation, large working bandwidth and
capability of detecting multi-directions of physical signals.
As such, silicon carbide and other wide band gap semiconductor nano-wires are also expected to be utilized in the near
future for integration within nanosystems operating at high
temperature conditions.
One alternative trend in the sustainable development of
thermal sensors is to investigate low-cost materials for thermal
sensors, which can be processed using cleanroom-free facilities and user-friendly techniques, without using toxic solvents
and hazardous chemicals. For example, the thermoresistive
effect in pencil graphite has been intensively investigated,
and a proof of concept of thermal flow sensors has been
successfully demonstrated. This indicates a possible future
982
JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 26, NO. 5, OCTOBER 2017
development of graphite-based thermal sensors such as convective accelerometers. Furthermore, future techniques for
improving the adhesion of pencil graphite to a substrate, or a
covering technique for protection of the graphite sensing layer,
are a potential research topic towards commercializing these
low cost thermal sensors.
ACKNOWLEDGMENT
This work was performed in part at the Queensland node of
the Australian National Fabrication Facility, a company established under the National Collaborative Research Infrastructure Strategy to provide nano and micro-fabrication facilities
for Australia’s researchers.
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Toan Dinh received the B.Eng. and M.Sc. degrees
from the Hanoi University of Science and Technology, Vietnam, in 2009 and 2012, respectively,
and the Ph.D. degree from Griffith University,
in 2017. He is currently a Research Fellow with
the Queensland Micro- and Nanotechnology Center,
Griffith University. His research interests include
micro/nano-electromechanical systems, physics of
semiconductors and sensors for harsh environments,
soft robotics, and advanced functional materials
for wearable applications. He was a recipient of
GUPRS, GUIPRS, and PAS scholarships from Griffith University.
Hoang-Phuong Phan received the B.E. and M.E.
degrees from the University of Tokyo, Japan, and
the Ph.D. degree from Griffith University, Australia.
He is currently a Research Fellow with the
Queensland Micro and Nanotechnology Center,
Griffith University. His main interests focus on
silicon carbide MEMS/NEMS for applications in
harsh environments. He has also been a Visiting
Scholar at the National Institute of Advanced
Industrial Science and Technology, Japan, in 2016,
and Stanford University, CA, USA, in 2017. He has
authored over 50 peer-reviewed journal articles and conference papers, two US
patents, and one book, all in micro and nanotechnologies. He was a recipient
of the Japanese Government Scholarships (MEXT) for undergraduate and
postgraduate studies (2006-2013), and the GUPRS and GUIPRS scholarships
from Griffith University for the doctoral course (2013-2016). He received the
GU Publication Award, the GGRS-IEIS travel grant, the Springer outstanding
theses Award, and the Australian Nanotechnology Network Oversea
Fellowship. He was also selected to the Australian delegates to attend the
23rd World Micromachines Summit in Barcelona, Spain, in 2017. He has
served as a Reviewer for several journals, including IEEE J OURNAL OF
M ICROELECTROMECHANICAL S YSTEMS , Sensors and Actuators A,
Micromachines, Material Science and Engineering B, the IEEE S ENSORS
J OURNAL, and IEEE E LECTRON D EVICE L ETTERS .
Afzaal Qamar received the M.Sc. degree in applied
physics from the University of Engineering and
Technology, Lahore, in 2004; the M.Phil. degree
in physics from the Pakistan Institute of Engineering and Applied Sciences, Islamabad, in 2006, on
a national competitive fellowship; and the Ph.D.
degree from the Queensland Micro- and Nanotechnology Centre, Griffith University, Australia, on
a competitive international scholarship. He served
as the Manager Technical for IIIV semiconductors
device fabrication at the Institute of Applied Technologies from 2008 to 2014. He also served as a Research Associate at
Griffith University. He is currently a Research Fellow with the Department
of Electrical Engineering and Computer Science, University of Michigan,
USA. His research interests are semiconductor physics, micro/nano devices,
thin films, MEMS/NEMS, and piezoresisitve and piezoelectric properties of
wide bandgap semiconductors. He has authored over 35 peer-reviewed journal
articles on these areas.
Peter Woodfield received the Ph.D. degree from
Sydney University, in 2001. He is currently a Senior
Lecturer with the School of Engineering, Griffith
University, Australia. He has extensive experience
in the fields of experimental and computational heat
transfer, computational fluid dynamics, thermophysical and transport property measurement techniques,
jet impingement quench cooling, and inverse heat
conduction problems.
Nam-Trung Nguyen received the Dipl.Ing.,
Dr.-Ing., and Dr.-Ing. habilitation degrees from
the Chemnitz University of Technology, Germany,
in 1993, 1997, and 2004, respectively. In 1998,
he was a Post-Doctoral Research Engineer at the
University of California at Berkeley, Berkeley,
USA. From 1999 to 2013, he was an Associate
Professor at Nanyang Technological University,
Singapore. Since 2013, he has served as a Professor
and the Director of the Queensland Micro- and
Nanotechnology Center with Griffith University,
Australia.
Dzung Viet Dao received the Ph.D. degree
in microelectromechanical systems (MEMS) from
Ritsumeikan University, Japan, in 2003. He was at
Ritsumeikan University as a Post-Doctoral Research
Fellow from 2003 to 2006, a Lecturer from 2006 to
2007, and the Chair Professor from 2007 to 2011.
In 2011, he joined as a Senior Lecturer with the
School of Engineering, Griffith University, where he
is currently teaching in Mechatronics and Mechanical Engineering. He is a member of the National
Committee on Mechatronics, Engineers Australia.
He has authored over 280 papers in scientific journals and conference
proceedings, and filed 15 patents. His current research interests include
Sensing properties in nanostructures, MEMS sensors and actuators, silicon
carbide transducers for harsh environment, and mechatronics.