JOURNAL OF MICROELECTROMECHANICAL SYSTEMS 1 ...€¦ · However, the fabrication of these sensors,...

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS 1

Thermoresistive Effect for Advanced ThermalSensors: Fundamentals, Design Considerations,

and ApplicationsToan Dinh, Hoang-Phuong Phan, Afzaal Qamar, Peter Woodfield, Nam-Trung Nguyen, and Dzung Viet Dao

Abstract— Microelectromechanical systems sensors have beenintensively developed utilizing various physical concepts, such aspiezoresistive, piezoelectric, and thermoresistive effects. Amongthese sensing concepts, the thermoresistive effect is of interestfor a wide range of thermal sensors and devices, thanks toits simplicity in implementation and high sensitivity. The effectof temperature on the electrical resistance of some metals andsemiconductors has been thoroughly investigated, leading to thesignificant growth and successful demonstration of thermal-basedsensors, such as temperature sensors, convective accelerome-ters and gyroscopes, and thermal flow sensors. In this paper,we review the fundamentals of the thermoresistive effect in metalsand semiconductors. We also discuss the influence of design andfabrication parameters on the thermoresistive sensitivity. Thispaper includes several desirable features of thermoresistive sen-sors and recent developments in these sensors are summarized.This review provides insights into how it is affected by variousparameters, and useful guidance for industrial designers in termsof high sensitivity and linearity and fast response. [2017-0022]

Index Terms— Thermoresistive effect, semiconductor, metal,two-dimensional (2-D) material, thermal sensor, temperaturesensor, thermal flow sensor, convective accelerometer, gyroscope.

I. INTRODUCTION

FOR MORE than three decades, MEMS (Micro Electro-Mechanical Systems) sensors have been developed aiming

at high sensitivity, fast response, stability and reproducibility,miniaturization capability and mass production. The workingprinciple of these sensors is based on a variety of physicalphenomena such as thermoresistive, piezoresistive, pseudo-hall, thermoelectric and piezoelectric effects [1], [2]. Amongthese effects, the thermoresistive effect, which refers to theelectrical resistance change with temperature variation, hasmany advantages in terms of simplicity in design and imple-mentation. Based on this effect, various micro-sized thermalsensors, which can monitor temperature [3], flow [4], [5] andacceleration [6], [7], have been successfully fabricated, thanksto the advancement in MEMS technologies.

Manuscript received January 26, 2017; revised April 26, 2017; acceptedMay 26, 2017. Subject Editor P. M. Sarro. (Corresponding author:Toan Dinh.)

T. Dinh, H.-P. Phan, A. Qamar, D. V. Dao, and N.-T. Nguyenare with the Queensland Micro-Nanotechnology Centre, Griffith Univer-sity, Nathan, QLD 4111, Australia (e-mail: [email protected];[email protected]).

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 availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2017.2710354

To date, a number of thermal sensing materials have beenemployed for developing thermal sensors, including met-als (e.g. platinum and nickel) and semiconductors (e.g. siliconand polysilicon) [5], [8]. For example, platinum has beenused for constructing thermal flow sensors, owing to its linearthermoresistive response, compatibility with microelectronictechnologies and relatively high positive temperature coef-ficient of resistance (TCR) [8]. In addition, semiconductorscould also be deployed for thermal sensors, thanks to theirwide range of TCR values from positive to high negative.Interestingly, the TCR of semiconductors can be tuned usingdifferent doping levels [9] or changing growth parameters [10].

However, the fabrication of these sensors, which requiresexpensive materials, clean room facilities and special-ized wafer processing equipment, has increased their cost,especially for small-scale production [11], [12]. Moreover,the fabrication of thermal flow sensors have involved varioussolvents and chemicals which are unfriendly for the environ-ment and could lead to contamination issues. In addition, thesesensors are unable to work in harsh conditions such as high-temperature and corrosive environments. Therefore, there isa strong demand for investigating alternative novel thermalsensing materials for advanced thermal sensors. Desirablecharacteristics for these sensors would be (1) low cost andhigh sensitivity, (2) linear response, stability and sustainability,(3) capability of working in harsh environments such as athigh temperatures and (4) flexibility and suitability for a widerange of applications, including the emerging field of wearableapplications.

The present paper reviews the fundamentals of the themore-sistive effect (Figure 1, top-left), and the impact of designand fabrication parameters on its sensitivity (Figure 1, top-right). The desirable features for thermoresistive sensors suchas sensitivity, linearity and response time are also mentioned(Figure 1, bottom-right). In addition, the applications of thiseffect for thermal sensors, including temperature sensors, ther-mal flow sensors and convective accelerometers/gyroscopes,are presented (Figure 1, bottom-left). Finally, current trendsand perspectives for the development of the thermoresistiveeffect and its applications are discussed. This review pro-vides useful design guidance to engineers and researcherswho are working on the development of thermal sensors.Following, section 2 revisits the fundamental aspects of ther-moresistive effects, including those in semiconductors andmetals. 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.


2 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS

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 parametersare the doping concentration, the material and morphology,the deposition temperature, the grain size and thickness.Section 4 considers the desirable features for thermoresistivesensors, including sensitivity, linearity, time response, powerconsumption and stability. Finally, section 5 discusses typicalapplications of the thermoresistive effect such as temperaturesensing, flow sensing and acceleration sensing.

II. FUNDAMENTALS OF THERMORESISTIVE EFFECT

In general, the electrical resistance of a homogeneousbar or film can be expressed in terms of its resistivity andgeometry as follows:

R = ρl

wt(1)

where R and ρ are the electrical resistance and resistivity ofthe material, respectively; l, w and t are the length, width andthickness of the bar/film, correspondingly. Based on Eq. 1,the resistance change (in the limit of small changes) canbe calculated depending on the resistivity change and thedimension changes [13], [14]:

�R

R= �ρ

ρ+ �l

l− �w

w− �t

t(2)

The change in each dimension (e.g. length, width andthickness), under a temperature variation, is the same becauseof the homogeneous property of the material. This dependson the thermal expansion coefficient (TEC, α) of the bar/filmas �l/ l = �w/w = �t/t = α�T , where �T = T − T0 is

the temperature difference; T and T0 are the absolute temper-ature and reference temperature (normally room temperature),respectively. Moreover, the change in the electrical resistancecaused by the influence of the change in the surroundingtemperature is known as the thermoresistive effect. In addition,the resistance change under the effect of temperature variationis attributed to the geometric effects (α�T ) and the change inresistivity (�ρ/ρ) [14]:

�R

R= �ρ

ρ− α�T (3)

For common metals, while the change in resistivity rangesfrom 3,900 to 6,800 ppm/K, the geometric effects alonecontribute 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 contribu-tion of geometric effects to the TCR is less than 5 ppm/K andthe resistivity change depends upon various parameters suchas doping levels, morphologies and temperature ranges. It isimportant to note that the temperature ranges also influencethe TCR of metals. The common value of TCR for bulksemiconductors used for thermal sensing applications is fromseveral thousands to several ten thousands ppm/K [5], [15]. Forexample, 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 thestructure is employed for temperature sensing purposes. Thus,the TCR is commonly defined as [13], [14]:

T C R = �R

R

1

�T= �ρ

ρ

1

�Tor T C R = 1

R

d R

dT(4)


DINH et al.: THERMORESISTIVE EFFECT FOR ADVANCED THERMAL SENSORS 3

TABLE I

RESISTIVITY AND TCR OF METALS USED IN THERMAL-BASED SENSORS, AND IMPACT OF THERMAL EXPANSION ON TCR [5], [15], [89]

In addition, the resistivity and TCR of thin films also dependupon their thickness. For example, when the thickness of thefilm shrinks to the nanoscale (e.g. lower than 100 nm), itsresistivity increases significantly due to the increase in thenumber of defects and boundaries in the film [17]. In addition,the absolute TCR of thin-film semiconductors could alsoincrease with decreasing thickness because of the increase inthermionic emission of the trapped carriers in the thin film atelevated temperatures [17].

A high absolute TCR is desired for thermal sensing applica-tions, since a sensor made of a high TCR material commonlyperforms well, exhibiting corresponding high sensitivity. Thissection first discusses thermoresistive principles and thenreviews the thermoresistive effect in common sensing mate-rials 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]. Thethermoresistive effect arises because temperature affects thenumber of carriers and their mobility in conducting materials.In single crystalline materials, the number of free chargecarriers increases with the rise of temperature due to theirability to be excited by thermal energy. This leads to animprovement in electrical conductivity. However, the mobilityof the carriers decreases with increasing temperature due tothe scattering effect of lattice vibrations. Therefore, when thetemperature increases, the resistivity of the semiconductorsmay decrease (negative temperature coefficient of resistance -NTCR), or increase (positive temperature coefficient of resis-tance - PTCR), depending upon the change in the number ofcarriers and their mobility. This dependence can be expressedby [1], [2]:

1

ρ= σ = enμe + epμh (5)

where σ and e are the conductivity and electron charge,respectively; n and p are the electron concentration and holeconcentration; respectively; μe and μh are the correspondingelectron mobility and hole mobility.

Figure 2 shows three temperature-dependent regions forthe resistivity of semiconductors. At sufficiently low temper-atures (extrinsic region), more carriers (n ∼ T αex p(Ed/kT ),where Ed is the activation (ionization) energy of donors,

Fig. 2. Temperature-dependent resistivity in semiconductors.

α is a constant and k is the Boltzmann constant, forn-type Si, α = 3/2) would be generated by thermal energyand excited to jump to the conduction band (CB). This isapart from existing carriers, which would always contribute toelectrical conductivity. In addition, lattice scattering causes aslight reduction of mobility (μ ∼ T −β , where β is a constant,for extrinsic silicon β = 3/2). The combination of the carrierconcentration and mobility can lead to a decrease in electricalresistivity (a negative TCR). Therefore, the electrical resistanceR of n-type semiconductors can be expressed in the followingform [1], [18]:

R = Aex p

(Ed

kT

)(6)

where A is a constant. The decrease in electrical resistivity inthe extrinsic region can be determined by a slope of Ed/k.However, at a higher temperature range (metal-like region),the free carrier concentration is saturated while the carriermobility still decreases [19]. This region exhibits a positiveTCR. In addition, at the highest temperature range (intrin-sic region), a significant number of bonds are being rup-tured and the carrier concentration increases. As a result,the temperature-dependent resistance of semiconductors iscommonly described as R = R0ex p

(Eg

2kT

), where Eg is the

energy gap, and the slope of Eg/2k defines the decrease ofresistivity in this region.

For semiconductor temperature sensors, the temperaturedependence of electrical resistance is generally used in the



following form [1], [2], [19]–[21]:

R = Aex p

[B

(1

T− 1

T0

)](7)

where A is a constant; B is the thermal index, which is used toevaluate the sensitivity of the thermoresistive effect in thermis-tors, as an alternative parameter to the TCR. B is calculated asEg/2k for semiconductors in the intrinsic region and Ed/k forn-type semiconductors in the extrinsic region. The relationshipbetween B and TCR can be written as B = −T C R × T 2

[1], [2], [19]. In the following subsections, we discuss thethermoresistive effect in several different materials for nicheapplications.

1) Thermoresistive Effect in Silicon and Silicon Nanos-tructures: It is well-known that Si has been a main-streammaterial for conventional thermal sensors such as thermal flowsensors and convective accelerometers. The thermoresistiveeffect in Si has been investigated in terms of temperaturedependence of resistivity, carrier concentration and carriermobility [22]–[30]. For example, the resistivity of in highlydoped silicon increases with increasing temperature, due to thedominance of the scattering effect, and then decreases whenthe temperature is high enough for providing thermal energyto break silicon bonds and generating more carriers.

Recent research has focused on the physical effect of Si atnano-scale levels since the carrier mobility of Si nanostructuressignificantly depends their surface-area-to-volume ratio [31].Great effort has been made for the development of siliconnanowires (SiNWs) fabricated using bottom-up and top-downapproaches [32]–[34]. However, the thermoresistive sensitivityof these SiNWs has been found to be similar to that of bulkand micro-level silicon devices [35], [37], [38]. For example,Wang et al. [35] reported a TCR of SiNWs fabricated bya bottom-up vapor-liquid-solid (VLS) process, which rangesfrom -3,700 to 120 ppm/K. As these TCR values are relativelylow and not of interest for thermal sensing applications,achieving a higher thermoresistive sensitivity and the abilityto integrate into nano-systems would be a trend in the devel-opment of thermoresistive devices. We used a Focused IonBeam technique to fabricate SiNWs (Figure 3(a)) by locallyamorphizing the single crystal structure, then employed anannealing process to recrystallize the structure for improvingthe electrical conductivity [36] (Figure 3(b)). This top-downprocess has resulted in a nanocrystalline structure for theSiNWs (Figure 3); hence a high thermoresistive sensitiv-ity of up to -12,000 ppm/K was observed for the SiNWs(Figure 3(c,d)). However, the thermoresistive properties ofSi are significantly degraded at high temperatures. Therefore,alternative materials such as silicon carbide have been inves-tigated, and showed potential for thermal sensors operating inharsh conditions. The following section will discuss the currentstatus of the thermoresistive effect in silicon carbide.

2) Thermoresistive Effect in Silicon Carbide (SiC) forThermal Sensors Operating in Harsh Environ-ments: Silicon carbide (SiC) is one of the most promis-ing candidates for thermal-based sensors operating in harshenvironments, due to its large band gap and superior phys-ical properties [39]–[43]. The thermoresistive effect in SiC

Fig. 3. Thermoresistive effect in SiNWs. (a) A 10 μm×0.2 μm× 0.06 μmSiNW fabricated by a Focused Ion Beam method. (b) Nanocyrstallinestructure of the SiNW examined by High-Resolution transmission electronmicroscopy (HRTEM). (c) Relative resistance change of the SiNWs. (d) TCRof the SiNWs. Reproduced from [34] and [36] with permission from the RoyalSociety of Chemistry and Elsevier.

Fig. 4. Thermoresistive effect in SiC. (a) Scanning electronmicroscopy (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 andTCR of a-SiC [54]. (d) Arrhenius plot of thermoresistance in a-SiC [54].Reproduced from [48] and [54] with permission from the Royal Society ofChemistry.

has been investigated in terms of the temperature effecton carrier concentration and its mobility in crystalline SiC[44]–[46]. In p-type 3C-SiC, the hole mobility is limitedby acoustic phonon scattering above 300 K and by ionizedimpurity scattering at temperatures below 250 K [44], [45],following the rule μH ∼ T −β , where β value ranges from1.2 to 1.4. In addition, highly doped n-type 3C-SiC has apositive TCR from 400 to 7,200 ppm/K [47]. Up-to-date, mostof high quality 3C-SiC has been grown on Si substrate withlarge area and low cost. However, a large current leakage tothe substrate was observed at temperatures above 100 ◦C [48],indicating that SiC on Si platform is not suitable for thermalsensors at high temperatures. Therefore, SiC films have beentransferred on to a glass substrate [48] (Figure 4(a)) to avoid



the current leakage. The thermoresistive properties of SiC onglass has been investigated with a relatively high temper-ature coefficient of resistance of up to -5,500 ppm/K [48](Figure 4(b)). Another advantage of SiC is that its the-moresistive properties are not affected by the visible lightillumination [49]. In addition, we proved that the thermore-sistive effect can tune the sensitivity of SiC material tostress/strain [50].

The hole mobility of other polytypes (6H-SiC and 4H-SiC)was also investigated, and followed the same rule as thatof 3C-SiC, but with a stronger dependence on temperature,in which the β value ranges from 2 to 2.6 [51], [52]. Thehypothetical reason is that the electron mobility of thesepolytypes at high temperatures is restricted by intervalley scat-tering and acoustic phonon scattering. However, the mobilityof 3C-SiC is limited by acoustic phonon scattering, and littleaffected by intervalley scattering, owing to the crystal sym-metry of 3C-SiC. These scattering phenomena would affectthe temperature-dependent resistivity of n-type and p-type6H-SiC. For example, Okojie et al. [53] reported a variationof TCR from -3,400 to 5,600 ppm/K, which depends upon thesemiconductor type and the doping levels.

Recently, the thermoresistive effect in amorphous SiC(a-SiC) has been investigated [54], showing a very largenegative TCR of from -16,000 to -4,000 ppm/K (Figure 4(c)).By analyzing the themoresistive properties of a-SiC, the energycharacteristics of this system were investigated with twoactivation thresholds of 150 and 205 meV, corresponding totemperature ranges of 300 to 450 K and 450 to 580 K,respectively (Figure 4(d)).

3) Thermoresistive Effect in Graphite for Low-Cost andEnvironmentally Friendly Thermal Sensors: As discussedin the previous sections, metals and semiconductors havebeen employed for conventional thermal sensors. However,these expensive materials have commonly involved complexprocesses and toxic chemicals. Therefore, there is a strongdemand to investigate the low cost and environmentallyfriendly materials for thermal sensors. Graphite is well-knownfor this purpose because of its ubiquitousness and relativelyhigh temperature coefficient of resistance (TCR) [55]. TheTCR of graphite was observed to be positive [56], whichwas explained based on the spacing of stacking faults ingraphite [57], tunneling conduction, impurity-assisted hoppingconduction and a combination of hopping and scattering ofcarriers by phonons [56]. However, a number of other studiesindicated a negative TCR for different types of graphite, whichcould be attributed to the defects and boundaries in graphite[58]–[60]. A negative TCR of approximately -3000 ppm/K wasobserved for temperatures of up to 200◦C and a positive TCRfor higher temperatures [61]. Other studies have also reportedthe thermoresistive effect in graphite at lower temperatureranges [62], [63].

Alternatively, the thermoresistive effect in graphite inkshas been reported [64], [65], showing a positive TCR oflower than 2200 ppm/K. However, pencil graphite showed arelatively high negative resistance change from -2,900 to -4,400 ppm/K (Figure 5), which is comparable to that of com-mon temperature sensing materials such as platinum, copper

Fig. 5. Thermoresistive effect in graphite [66]. (a) Graphite resistance changeas a function of temperature. (b) Temperature coefficient of resistance (TCR)of pencil graphite. Reproduced from [66] with permission from the RoyalSociety of Chemistry.

Fig. 6. Thermoresistive effect in carbon nanotubes [75]. (a) CNT resistancechange as a function of temperature. (b) Temperature coefficient of resis-tance (TCR) of CNT. Reproduced from Ref. [75] with permission from theRoyal Society of Chemistry.

and nickel [66]–[68], which was explained based on the theoryof the boundary between graphite crystallites (referred toFigure 8(b), “C. Material choice and impact of morphologies”section). In this theory, carriers are excited by thermal energycan pass through or pass over the barrier between graphitecrystallites, which lead to an increase in the electrical conduc-tivity of graphite.

4) Thermoresistive Effect in Carbon Based Nano-Materials:Recent studies have paid attention to the thermoresistive effectin nano-materials such as carbon nanotubes (CNTs) [69]–[72]and graphene [73], [74]. However, thermoresistive sensitivi-ties of these materials are relatively low (e.g. absolute TCRvalues are commonly lower than 1250 ppm/K). In addition,the current difficulties in releasing these materials make themchallenging to use in Joule heating based thermal sensors.To date, few studies have demonstrated the use of these mate-rials in Joule heating based thermoresistive sensors [75], [76].Figure 6 shows the thermoresistive effect in CNT yarns witha TCR of approximately 750 ppm/K, which has been usedfor temperature and flow sensing applications [75]. In somecases, when these materials are mixed with others to make acomposite (e.g. epoxy/MWCNT composite, multi-walled car-bon nanotubes (MWCNTs)/styrene-b-(ethylene-co-butylene)-b-styrene (SEBS) triblock copolymer), their thermoresistivesensitivity can increase and they are potential candidates forhighly sensitive temperature sensors [20], [71], [72].

5) Thermoresistive Effect in Compounds and Other Mate-rials: It is important to note that a giant thermoresistanceis desired for thermal sensing applications, and this canbe achieved using ceramics and nanocomposites. As such,



the giant thermoresistance with a temperature coefficient ofresistance of up to -6%/K (the thermal index B is from2000 to 5000 K) was achieved [3], [77]. In the temperaturesensing area, it is well-known that ceramic thermistors havebeen commercially available thanks to their high sensitivityand accuracy and low cost [3]. In contrast to Si-based tem-perature sensors, oxide semiconductor (ceramic) thermistorshave a carrier concentration, which is solely determined bythe doping levels; however, the carrier mobility is thermallyactivated with increasing temperature and the increase in theconductivity is mainly due to hopping of carriers betweenlocalized states in the mobility gap. This leads to an extremelylarge thermoresistive effect in ceramic thermistors.

Different giant positive temperature coefficients ofresistance have been reported for various nano-composites[78]–[83], in which the conduction mechanism is mainlybased on a volume expansion of the composites. Thisleads to an increase of the distance between conductive nano-tubes or nano-particles, or a breakage of conductive pathways.Therefore, a positive temperature coefficient of resistance hasbeen commonly observed for the nano-composites. In somecases, when the electrons in nano-composites are providedenough thermal energy by the increasing temperature, theycan tunnel over the separating gaps and the conduction of thecomposites is thermally activated with a negative TCR [78].

Recently, two-dimensional (2D) materials such as transitionmetal dichalcogenides (e.g. MoS2, MoSe2 and WS2) haveattracted much interest for electronics and sensors, owing totheir excellent mechanical, electronic, optoelectronic proper-ties and potential for extremely low power consumption. Thesematerials are constructed based on the arrangement of atomiclayers. The electrical conductivity along c-axis (perpendicularto the atomic layers), σ||, is less than that perpendicular toc-axis (σ⊥) and depends upon the number of layers [84]–[86].When the number of layers decreases to a few (e.g. single layerand bi-layer), the contribution of σ|| is significant. In this case,it has been proven that the tunability of σ|| by electrical fieldenables high-performance electronics (e.g. transistors) [87].In addition, the tunability of σ|| by thermal energy (or tempera-ture) can enhance thermoresistive properties of these materials.However, the state-of-the-art results on thermoresistive effectsin 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 potentialof 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 temperatureincreases, but the mobility of the existing carriers decreaseslinearly (μe ∼ T −1), due to the scattering effect. As a result,the resistivity or resistance R increases linearly with increasingtemperature (ρ ∼ T ) as follows:

R = R0 (1 + T C R(T − T0)) (8)

where R0 is the electrical resistance at reference tem-perature T0. Therefore, metals commonly show a positive

temperature coefficient of resistance (TCR) [5], [15], [88].Table I shows the TCR of several common metals, whichare commonly used for thermal sensing applications [5], [15].The data from the I indicates positive TCR values rangingfrom 4000 to 7000 ppm/K and a geometric effect of less than30 ppm/K.

III. IMPACT OF DESIGN AND PROCESS ON PERFORMANCE

OF THERMORESISTORS

High-performance thermoresistors are needed to achievehighly sensitive thermal sensors. For example, the sensitivityof thermoresistors strongly depends on the substrates on whichthese thermoresistors are fabricated. Moreover, doping typeand doping level play an important role in determining thesensitivity of semiconducting thermoresistors. The dependenceof sensitivity is expanded to the morphology (e.g. crystalline,polycrystalline and amorphous structures) of the thermoresis-tive materials. In addition, designers should also pay attentionto grain size of thermoresistors in choosing deposition tem-perature and thickness of thermoresistors.

A. Substrate Influence

For bulk materials, a substrate to support constructing ther-moresistive devices is not commonly required. However, forthin film thermoresistive sensors, there is an additional thermalexpansion mismatch between the films and their supportingsubstrates. This effect of substrates on the thermoresistiveproperties of thin films plays an important role in the accuracyand sensitivity of such devices [14], [15], [90].

There are various studies, which have aimed at evaluatingthe influence of the substrate on the thermoresistive propertyof the thin films [14], [15], [90]–[92]. As such, Hall et al. [14]suggested a contribution of 65 ppm/K for thin films supportedby glass substrates and a replacement for soft glass of fusedquartz can shift the TCR to 36 ppm/K. This effect is quitesignificant, since the TCR of typical thin films is lower than100 ppm/K. Similarly, Verma et al. [15], developed a generalequation for estimating the impact of thermal strain on thethermoresistive effect in thin films as follows:

� = −2(αl f − αls)

1 − μ f

[γ (1 − μ f ) + μ f (1 − γ )

](9)

where � is the difference between TCR of thin films withand without substrates, αl f and αls are the thermal expansioncoefficient of films and substrates, respectively; μ f and γ arethe PoissonâŁ™s ratio of thin films and the strain coefficientof resistivity (G F), respectively.

To date, very limited work is available on the impactof semiconducting substrates on the thermoresistive proper-ties [93]. On one hand, the current leakage to the semicon-ducting substrates at elevated temperatures would make thesemiconducting substrates not suitable candidates for ther-moresistive sensors at high temperatures [93]. In addition,it is required to isolate the thermoresistive sensing elementsfrom the heater and reduce the power loss to the substrate.Therefore, the thermoresisisive sensors are commonly devel-oped on suspended membranes or insulation substrates such as



TABLE II

ACTIVATION/IONIZATION ENERGY OF IMPURITIES IN SEMICONDUCTORS [98]–[110]

glass, alumina, fused quartz and silicon nitride [14], [94], [95].In many cases, silicon dioxide (or glass) membranes are prefer-able as supporting layers for thermoresistive sensors becausesilicon 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 thermalconductivity would minimize the conduction heat loss to thesubstrate.

On the other hand, a semiconducting substrate could be alsoused as an active layer, and the combination of the substrateand the functional layer can create other electronic devicessuch as diodes [96]. The thermoresistive behavior betweenthese layers has been used for highly sensitive temperaturesensors. A detailed review on these devices can be foundelsewhere [97].

B. Doping Influence

1) Doping Type: As previously mentioned, the thermore-sistive sensitivity depends upon the activation energy (orionization) energy of dopants. As such, a dopant with highactivation energy Ed (or Ea) can provide a large temperaturecoefficient of resistance (T C R = −Ed/T 2) or a large slopeEd/k. The activation energy of donors or acceptors can becalculated using band gap theory [2]. Nitrogen has beencommonly 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 (Ed and Ea)for various impurities in Si and silicon carbide [98]–[110]at room temperature. Doping in semiconductors refers to theintroduction a small amount of impurities into the crystal toincrease the number of carriers that are excited by thermalenergy and contribute to the electrical conductivity [1], [2].In contrast, the doping in ceramics (a mixture of metaldioxides) refers to the substitution of impurities into chemicalsites (e.g. metal or oxygen ions), which leads to changesin the way electrons ’hop’ between ions of the chemicalspecies [3], [111], [112].

2) Doping Level: There are various studies on the dopingdependence of activation energy. It has been reported thatactivation energy decreases with increasing doping levels [26],[113]–[115]; hence there is a decrease in the thermoresistivesensitivity. Lopatiuk-Tirpak et al. [113] reported a reduction ofactivation energy of p-type ZnO from 212 to 135 meV with anincrease in the doping level from 1.3×1017 to 1.3×1018 cm−3.The dependence of this activation energy on doping levels isattributed to the formation of the band-tail states, which extendinto the forbidden gap and the expansion of the acceptor band.

Fig. 7. Impact of doping levels on the thermoresistive effect in semiconduc-tors. (a) Doping dependence of the thermoresistive effect in polysilicon [9].Reprint with permission from [9]. (b) Doping dependence of the thermoresis-tive effect in silicon carbide [118].

It was also hypothesized that this dependence is due to theCoulomb interaction between holes in the valence band (VB)and the ionized acceptor states, which leads to the reductionof binding energy. A similar behavior of Si-doped n-typedGaN was reported, exhibiting a reduction of activation energyfrom 28 to 21 meV with carrier concentrations increasing from7.25×1017 to 1.6×1019 cm−3 [114]. An activation energyof 40 to 54 meV was reported for SiC [116], also dependingon the doping level.

The thermoresistive sensitivity of other materials such assilicon and silicon carbide can be controlled by adjustingdoping levels [9], [47], [53], [117]. Seto et al. [9] reporteda significant improvement in the thermoresistive sensitivityof polysilicon with decreasing doping levels. At low dopingpoints (e.g. ∼ 1016 cm−3), the ionization energy is almosthalf the energy gap value (approximately 0.5 eV) of singlecrystalline silicon while it reduces to 0.025 eV at a highdoping level of 1019 cm−3 (Figure 7(a)). The mechanism ofthis effect was hypothesized based on a decrease in the barrierheight and barrier width with increasing doping levels. TheTCR value of silicon was also reported to depend upon dopinglevels [116]. As such, when decreasing the doping level from1018 to 1014 cm−3, the TCR value reduces from approximately8000 ppm/K to almost 0 ppm/K at room temperature.

Furthermore, Shor et al. [47] have reported the dopingdependence of 3C-SiC resistivity. At unintentional dopinglevels, all impurities are ionized below room temperature,and the resistivity increases (T C R ∼ +0.72% /◦C) withincreasing temperatures above room temperature due to thedominant scattering effect. However, at low doping levels,the temperature at which the resistivity reaches a mini-mum value, is higher (around 200 ◦C). In the case ofdegenerately doped 3C-SiC, all impurities are ionized at all



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 dopingon the thermoresistive effect in 3C-SiC (Figure 7(b)), showingan increase in the thermoresistive sensitivity with decreasingdoping levels of nitrogen. The change of 6H-SiC resistivitydepending on doping levels has been also investigated [53].For instance, a low doping level (1017 cm−3) is fully ionizedat 0◦C, while a high doping level (1019 cm−3) has a higherionization temperature of 500 ◦C. At the same doping levelof 2 × 1019 cm−3, the p-type 6H-SiC shows a higher absoluteTCR in comparison with the n-type. Also with high dopinglevels, impurity scattering is considered to be the dominantmechanism.

C. Material Choice and Impact of Morphologies

1) Material Choice: In general, the use of thermoresis-tive materials for developing thermal sensors depends uponexpected performance and applications. A large thermore-sistive effect (i.e. large TCR) is desired for thermoresistivesensors in terms of sensitivity. Nanocomposites and compoundmaterials (mentioned in Section II. A) are potential candidatesfor this purpose; hence they are commonly employed assensitive temperature sensors [78]–[83]. However, the dis-advantages of these materials are the non-linear and hys-teresis characteristics, which require additional circuitry andcomplex processing of sensor signals for accurate measure-ments. In addition, these materials have large resistivity; hencethey are not suitable for the thermal-based sensors such asthermal flow sensors and convective inertial sensors whichinvolve heating elements. To increase the temperature ofthe heating elements at low supply voltages, a low resis-tivity is required, which commonly lies between 10−1 to10−6 �cm [5]. Therefore, highly doped semiconductors (e.g.highly doped single crystalline silicon with resistivity from10−1 to 10−2 �cm) and metals (e.g. platinum nickel withresistivity is from 10−4 to 10−6 �cm) are the conventionalcandidates for these sensors. It is important to note thatsemiconductors and metals are compatible with conventionalMEMS micro-machining technologies, which leads to thecommercialization of various thermal-based sensors employ-ing these materials.

There is a strong demand to investigate alternative ther-moresistive materials which can first satisfy the basic require-ments: (1) high thermoresistive sensitivity, (2) low resistivityand 3) compatibility with MEMS machining technologies. Therequirements for these alternative materials are also low cost,ease of processing and ability to work in harsh environmentsincluding high temperatures, high corrosion and high voltages.Large band gap semiconductors such as silicon carbide arepromising candidates for thermal sensors operating in hos-tile environments thanks to corrosion inertness and superiormechanical and electrical properties [39]–[43], [119], [120],while carbon-based materials such as graphite are a goodchoice for low cost and rapid prototyping of thermalsensors [64]–[68].

2) Impact of Morphologies: There are three main morpholo-gies of thermoresistive materials, namely single crystalline,

Fig. 8. Transport mechanism in different morphologies. (a) Single crystalline.(b) Polycrystalline.

polycrystalline and amorphous configurations. Among these,single crystalline and polycrystalline materials can achievea reasonable low resistivity (e.g. 0.1 �cm for silicon) forheating purposes in various thermal-based sensors such asthermal flow sensors and convective accelerometers. In purecrystalline materials, the generation of carrier concentrationand the increase in carrier mobility with increasing tempera-ture play an important role in the behavior of the thermore-sistive effect (Figure 8(a)) [1], [2]. For example, in highlydoped single crystalline silicon, all impurities are ionized atroom temperature, and only scattering is considered at highertemperatures, which leads to a positive temperature coefficientof resistance (e.g. normally lower than 5,000 ppm/K).

However, a polycrystalline material is a complex compo-sition of crystallites and the boundaries between them [9],[121], [122]. Therefore, some models have been proposedto explain the resistivity dependence on polycrystalline mor-phology. As such, Seto [9] hypothesized that boundaries inpolycrystalline material can trap carriers, creating a potentialbarrier φ to impede the movement of carriers through thebarrier. Therefore, the boundary resistance plays an dominantrole in the thermoresistive effect of polycrystalline material.The boundaries are sensitive to temperature change as bothtunnelling and thermionic emission mechanisms can contributeto a decrease in electrical resistance with increasing tempera-ture (Figure 8(b)). When the polycrystalline material is dopedat high levels, the barrier is low; hence the thermionic emissionmechanism is dominant. The thermoresistive sensitivity wasobserved to be low in highly doped polycrystalline silicon.The model proposed by Seto [9] has been used to explain thehigh thermosensitivity of various polycrystalline materials [9],[121], [122]. The temperature-dependent electrical resistanceR of poly/nano crystalline structures can be determined by thefollowing equation:

R = Aex p

(φ

kT

)(10)

where k is the Boltzmann constant, R is the electri-cal resistance at temperature T , and A is a constant.In polycrystalline metals, the grain boundary plays adominant 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 lessthan the bulk value and it could turn to a negative value ifthe TCR of bulk material is less than temperature coefficientof bulk mean free path [15], [92]. In ceramics, the role



of grain boundaries on the thermoresistive properties is stillcontroversial [123]–[125]. As such, it has been reported thatthe thermoresistive sensitivity of grain boundaries is muchhigher than that of bulk materials and more sensitive toannealing conditions [123]. However, some other reports haveshown that the activation energy of grain boundaries is thesame as that of bulk boundaries [124], [125].

Another important morphology of semiconductors is amor-phous, which is known for its localized and extended states.Amorphous semiconductors have an energy level betweenthem, named mobility edge. The extended and localized stateshave a different density of state (DOS), which can be a con-stant, parabolic or exponent function of temperature dependingon the temperature range. In a broad range of temperatureT , the conductivity σ of amorphous semiconductors can beexpressed in the form:

σ = σ0ex p

[−

(Ea

kT

)β]

(11)

where σ0 is the pre-exponential factor, and the powerexponent β depends on temperature range. Ea denotesthe activation energy and k is the Boltzmann constant.Mott et al. [126] developed the concept of variable-rangehopping (VRH) for the temperature-dependent conductivitywith the assumption of a constant DOS function. The value ofβ in Eq. 11 was found to be 1/4 for the VRH regime. However,due to the interactions between localized electrons, a Coulombgap exists in the DOS, which has a parabolic distribution atlow temperatures. As a result, β = 1/2 shows the presenceof the Coulomb gap [127]. At temperatures high enough (e.g.temperatures close to room temperature), the transport energymoves upward towards the mobility edge. Electron transitionsbetween the de-localized states above the mobility edge andthe localized band tail mainly contribute to the conductionof amorphous semiconductors [127]. The temperature depen-dence of conductivity is observed with β = 1, showing anactivation of electrons over the mobility edge [128]. Thismechanism has been used for investigating the thermoresistiveeffect in a-Si and a-Si:H, with TCR values ranging from -20,000 ppm/K to -80,000 ppm/K for a temperature rangeof 300 to 350 K [129]–[131].

D. Deposition Temperature, Grain Size and Thickness

In general, when deposition temperatures (or substratetemperatures) increase, the grain size of thermoresistor filmsincreases and the resistivity decreases. This could tune thethermoresistive sensitivity of the films [10], [132], [133]. Forexample, it has been reported that an increase in the depositiontemperature from 25 to 300 ◦C can change the TCR of CuNithin film resistors from negative (-50 ppm/K) to zero andthen positive (80 ppm/K) [10]. This could be attributed tothe enhancement of amorphization under lower-temperaturedepositions. It has been found that the crystallinity of thefilms degrades significantly when the substrate temperaturedecreases [10], [132]. For instance, Himanshu et al. [134]reported that improvement in crystallinity could be achievedwhen the deposition temperature increases from 350 to 850 ◦C;

Fig. 9. Influence of substrate temperature on the thermoresistive effect inSiC thin films [134].

Fig. 10. The dependence of thermoresistive effect on thickness of films.(a) Thickness dependence of TCR in platinum [136]. Reprint with permissionfrom [136]. (b) Thickness dependence of TCR in silicon carbide [17].

however, the thermoresistive sensitivity also decreases with adecrease in activation energy from 0.57 to 0.086 eV (Figure 9).

In addition, the thermoresistive effect in polycrystallinemetal 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 avery small grain size, but it could approach a large positivevalue (similar to the TCR of bulk material) by using a verylarge grain size [92].

It has been reported that the thermoresistive sensitivitydepends upon the thickness of thin films. For example, the ther-moresistivity of platinum nano thin films is lower than thatof bulk materials [136]–[138] (Figure 10(a)). However, forsemiconductor thin films such as SiC, it has been proven thatthe thinner the film thickness, the higher the thermoresistivesensitivity (or the higher the TCR) [17], [139]. This phenom-enon has been explained based on the free carrier trappingmodel [140], [141]. As such, thinner films normally havea smaller grain size and have more defects and boundaries,which make a potential barrier to impede the movement offree carriers. Both thermionic and tunnelling currents passingthis barrier contribute to the thermosensitivity of the ultra-thin films. Figure 10(b) shows the thickness dependenceof the TCR of SiC thin films, and indicates a TCR offrom -1400 ppm/K to 2200 ppm/K for the film thicknessof 16963 to 1530 A, respectively [17].



IV. DESIRABLE FEATURES FOR THERMAL SENSORS

For effectively realizing the thermoresistive effect for theapplications of thermal sensors such as temperature sensors,thermal flow sensors, convective accelerometers and gyro-scopes, several important features need to be considered in thedesign and implementation of thermal-based sensors. Theseare thermoresistive sensitivity, linearity of response, thermaltime response and other features.

A. Sensitivity

Among the desirable parameters for thermal sensors, sensi-tivity is one of the most important features because it repre-sents the efficiency of detection or monitoring. As previouslymentioned, the temperature coefficient of resistance (TCR)has been commonly used for evaluating the sensitivity of thethermoresistive effect, defined by relative resistance change tothe temperature variation. The units of TCR, often found inliterature, includes ppm/K (parts-per million per Kelvin) and%/◦C (percent per Celsius). Moreover, for temperature sensorsusing ceramic and semiconductor materials, the thermal indexB (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 tem-perature sensors; hence a ceramic material or a compos-ite/mixture is often deployed since these materials can providean extremely high TCR of up to 1012 ppm/K [82]. However,these materials might not be suitable for other thermal sensorsbased on the Joule heating effect, such as thermal flow sensorsand inertial sensors. This is due to the fact that these sensorsrequire a low resistivity to reduce the voltage or current supplyfor heating. Therefore, metals and highly doped semiconduc-tors have been commonly employed to fabricate this typeof sensors. However, these materials have some drawbacksin terms of low thermoresistive sensitivity (e.g. lower than5,000 ppm/K).

It is important to note that detecting temperature changes inthermal-based sensors which operate based on Joule heatingis quite challenging, since these sensors employ materialswith low thermoresistive sensitivity. Therefore, the resistancechanges (�R/R) in these sensors are commonly converted toa voltage change (�V ) by using a Wheatstone bridge, and thisvoltage change can be amplified using signal amplifiers.

Alternatively, a thermoresistive insensitivity or a zero tem-perature coefficient of resistance (TCR) is desired for theprecise control of temperature in heaters and other sens-ing applications including strain and pressure measurements.Many studies have focused on developing zero-TCR systemswith semiconductors and inorganic compounds [117], [118],[140], [142], [143]. For example, controlling doping levels hasbeen proven to be an effective approach to achieve zero-TCR,which is commonly done in the in situ growth process of thesemiconductor films [117], [118], [140]. However, a commonstrategy for achieving zero-TCR in polymers/composites is tomix a negative-TCR material with a positive-TCR material.For example, Chu et al. [142], [143] reported a near zero-TCRof conductive composites consisting of a bi-layer of negativeTCR carbon nanotube and positive TCR carbon black, showing

less than 2% variation of relative resistance change when thetemperature reaches 200 ◦C. In some cases, the effect of thesubstrates on the thin films is significant as it can tune theTCR from a negative [66] value to a positive value [144].

B. Linearity

Linearity is another desirable parameter for thermal-basedsensors, since it is responsible for the accuracy of mea-surement. Thermal sensors with linear characteristics havevarious benefits, not only in the accuracy of measurement,but also in terms of simplicity in the design of circuitry andimplementation.

Most metals show excellent linearity in a wide range oftemperatures; hence they have been commonly deployed forfabricating thermal flow sensors, convective accelerometersand gyroscopes. The reason for the linear characteristics ofmetals is that the number of electrons in metals is con-stant, while electron mobility is inversely proportional totemperature; hence using equation 5, the resistivity is linearlydependent on temperature.

However, the resistance of semiconductors is exponentiallydependent on temperature as shown in Eq. 7. Therefore,to realize the design of circuitry and the measurement ofsignals, Eq. 7 is usually converted to the following form,which presents the linear relationship between ln(R/R0) (Rand R0 are the electrical resistance at temperature T and T0,respectively) and 1/T :

ln (R/R0) = A − B

(1

T

)(12)

where A = B/T0 is a constant. Equation 12 has beencommonly used for representing the Arrhenius law. Fromplotting Eq. 12, the sensitivity of the thermoresistive effectB or the activation energy Ea = B × k, where k is theBoltzmann constant, can be determined. For example, Figure 7shows the linear relationship between ln(ρ/ρ0) and 1/kT ,indicating an activation energy of 0.025 eV to half energygap of single crystalline silicon. It should be noted thathighly doped semiconductors could also achieve a linearitybetween electrical resistance and temperature, since all impu-rities have the potential to be ionized at room temperature andthe resistance depends upon the scattering mechanism withchanging temperature [49]. This behaviour of highly dopedsemiconductors is similar to that of metals. Therefore, usinghigh doping levels for the Joule heating based sensors couldachieve a linear characteristic [16].

C. Thermal Time Response

Apart from the sensitivity and the linearity, thermal timeresponse is also considered as a key feature for thermalsensors, as it presents the capability to respond instantaneouslyto the change in external signals such as temperature, flowand acceleration. Theoretically, the thermal time response ofthermoresistive sensors is limited by the thermal time constantτ = Rth × Cth , where Rth and Cth are the thermal resis-tance and thermal capacitance of the sensor [145]. Thermalresistance can be calculated as Rth = L/(A × k), where



Fig. 11. Response time of thermal flow sensors. (a) The 63.2% responsetime of a sensor. (b) A thermal time response of 2.5 ms is determined fromfitting the equation T = A − B × exp(−t/τ ) [149]. Reprint with permissionfrom [149].

L, A and k are the length, cross-sectional area and thermalconductivity of the sensor material, respectively. A materialwith a higher thermal conductivity offers a lower thermalresistance; hence it has a faster thermal time response. Forexample, 4H-SiC would be preferable to Si for developingthermal sensors with fast thermal time responses because thethermal conductivity of 4H-SiC is much higher than that ofSi [146]. Thermal capacitance can be approximated as Cth =ρth × V × CH , where ρth , V and CH are the density, volumeand heat capacity of the sensor, respectively. The density ofsome metals such as platinum (ρth=21.45 g/cm3) is largerthan that of semiconductors such as silicon (ρth=2.33 g/cm3)and silicon carbide (ρth=3.2 g/cm3). However, platinum hasa much lower heat capacity (CH =125 J/(kgK)) in comparisonto silicon (CH =700 J/(kgK)). Therefore, a common strategyto achieve a fast thermal time response is to scale down thethermoresistive elements or choose materials with high thermalconductivity, low density and low heat capability. As such,nano structures (e.g. nanowires and nanobelts) would offerfast time responses which are useful for measuring systemswith rapid changes of temperature.

Experimentally, the thermal response time is commonlydefined as the time needed for the amplitude of the outputsignal to reach approximately 63.2 % or 90 % of that of asteady-state signal, due to a change of external parameters[94], [147], [148]. Figure 11(a) shows the response time of athermal flow sensor, which is determined by 63.2 % amplitudeof the steady-state signal [147]. The thermal response timecould also be determined from the exponential fit for the timedependence of temperature response T = A− B ×ex p(−t/τ),where A and B are constants; t and τ are the time parameterand the thermal time response, respectively [149]. Figure 11(b)shows the response time of τ=2.5 ms by fitting the response ofthe sensor [149]. For various MEMS thermal sensors reportedin the literature [94], [147]–[149], the thermal response timeis within the ms range, corresponding to a the bandwidth ofthe kHz range. These responses satisfy the practical applica-tions such as measuring human respiration, which requires themonitoring of 12 to 20 breaths per minute, corresponding toa bandwidth of only 0.2 to 0.33 Hz.

D. Low Power Consumption

Low power consumption is an obviously desirable fea-ture for not only thermal sensors but also other electronicdevices. This can be achieved through miniaturization, taking

advantages of micro and nanomachining technologies. Forexample, a small-in-size heater in thermal flow sensors couldbe heated up to a high temperature with low power because ofits small volume, which can also lead to a faster response ofthe sensor. For example, Cubukcu et. al. [150] has proven thatthe sensitivity of the sensor at a constant power consumption isimproved by scaling down the size of its structures. Therefore,nanostructures such as nanowires and 2D materials are ofinterest in terms of low power consumption and fast thermalresponse.

For thermal sensors not requiring a heating element suchas temperature sensors, a small size (e.g. length, width andthickness) is of interest as it leads to a faster response to tem-perature change and a more uniform temperature distributionwithin the sensor [75]. It is expected that when the size of thethermal sensor is scaled down to lower than a certain value(e.g. 100 nm), the thermoresisitive sensitivity could decreasedue to the impact of material morphologies at nanoscales[136]–[138]. However, for thermal flow sensors and inertialsensors which require heaters and thermoresistive sensing ele-ments, a longer (up to 1000 μm) and wider (up to 70 μm) heat-ing elements can result in a larger output signal from the sensordue to the reduced heat conduction to the substrate [149].However, a long heating element leads to a higher resistancewhich requires a higher supply voltage. In addition, a widerheating element offers a slower time response. The distancebetween heating and sensing elements is another importantgeometrical parameter which can have an even greater effecton the sensitivity and measurement range than the size of thesensor [151]. In some cases, T-shape sensing elements (withtwo ends free to expand or contract when the temperaturechanges) can be utilized for lowering the thermally inducedstress [152], [153].

With regards to design, themoresistive sensors fabricatedon suspending isolation substrates could reduce power loss incomparison to sensors located on thick substrates or semi-conducting substrates. To realize the suspended structures,electrodes and thermoresistive elements are commonly pat-terned first using conventional lithography and surface etchingprocesses; then wet etching of bulk substrates (e.g. silicon) isperformed from frontside or backside to release the membranestructures [94], [151].

A number of the thermal flow sensors could operate undersub-mW power consumption (lower than 1 mW) using sus-pending isolation structures, while these devices can maintaina large measurement range with high resolution and withoutloosing its fast time response [154], [155]. It is also importantto note that a decrease in the supply power leads to a lowersensitivity of such sensors. Therefore, a large thermoresistiveeffect is desired to achieve a high sensitivity and high resolu-tion of detection at low power consumption [150].

E. Stability and Other Desirable Features

For practical applications, the repeatability, long-termstability and ability to work in harsh environments with-out degradation of performance are also desirable fea-tures for thermoresistive sensors. Among these features, the



repeatability and stability are essential for the reliability andaccuracy of measurements. These desired characteristics arecommonly determined from repeated cycle tests. For example,Shingo Harada et al. [156] observed the consistence of theperformance of a flexible thermoresistive temperature sensorafter several repeated cycle tests at both the room temperatureand an elevated temperature. Thermoresistive structures aretypically placed outdoors where the temperature variation,humidity and chemical species are not controlled. This leadsto the drift or instability of the sensor signal. For exam-ple, when a ceramic thermoresistive element is exposed toatmospheric conditions, its surface chemically adsorbs anddissociates water vapor molecules to form layers of hydroxylions, followed by a physical absorption. This results in achange in the electrical conductivity of the themoresistiveelement [157]. Low porousity thermoresistive materials aredesirable for minimizing the impact of humidity on the resis-tive structures [3], [157]. A signal processing method has beenproposed to possibly eliminate the effect of humidity and otherfactors [158].

In addition, various metals (e.g. aluminum) and semicon-ductors (e.g. silicon) cannot operate in harsh conditions suchas high temperatures. This leads to a strong demand fordeveloping alternative thermoresistive materials, which areable to work in harsh environments. Wide band gap semicon-ductors have been recently studied with an aim towards hightemperature applications, due to their superior electrical andmechanical properties at high temperatures. For example, sili-con carbide has demonstrated excellent stability when exposedto 400 ◦C in air for 2000 hours [159].

V. APPLICATIONS OF THERMORESISTIVE EFFECT

The insight into the thermoresistive effect described in theprevious sections has led to various successful MEMS sensorapplications. Among them, thermal flow sensors have beenmainly developed using metals (e.g. platinum, gold and nickel)and semiconductors (e.g. silicon and polysilicon). The goodconductivity of these materials is required to measure thetemperature of the thermoresistors at a low voltage supply. Theresistance change of the thermoresistors induced by a flow or atemperature change around the sensor is used to determinecharacteristics of the flow. Another application of the ther-moresistive effect is the detection of acceleration. However,convective accelerometers, commonly employing metals andsemiconductors, work based on the movement of the bubblesof heated fluid around them, which leads to an asymmetryof the temperature profile. Therefore, these accelerometersrequire an enclosed chamber and thermoresistors around themto detect the change of temperature profile.

In addition, one of the most important applications ofthe thermoresistive effect is temperature sensing. Temperaturechange directly leads to the change in the electrical resistanceof thermoresistive materials. A number of materials have beendeployed for this purpose, namely metals, semiconductors,nanomaterials and other compounds/mixtures. Temperaturesensors could be employed for a wide range of materialsbecause these sensors do not require high conductivity like

thermal flow sensors and convective accelerometers whichwork based on the Joule heating effect. This section will dis-cuss in details the current status of development of thermore-sistive sensors such as temperature sensors, thermoresistiveflow sensors, convective accelerometers and other advancedthermal sensors based on the thermoresistive effect.

A. Temperature Sensors

In general, thermocouples, and metal and ceramic ther-mistors are commonly used as temperature sensors, and arecommercially available [3]. Ceramic thermistors, a type ofNTCR temperature sensors, have shown various importantadvantages in terms of high sensitivity, signal-to noise ratios,small size and low cost. The sensitivity of these temperaturesensors depends upon the grain size and the composition of themetallic oxides [3]. However, complexity in terms of the chem-ical composition, the formation of micro-structures and theoxidation processes has led to various difficulties in controllingthe processing parameters and the chemical homogeneity. As aresult, the process for achieving highly stable and reproducibleceramic thermistors is a significant challenge; hence, costs areraised, limiting their specific applications.

The aforementioned difficulties with the ceramic thermis-tors have resulted in a strong demand to develop sim-ple and single-film semiconductor thermistors, which arestable and reproducible, and avoid the use of chemicalmixes [159]–[164]. Efforts have been made to improve thesecharacteristics. For example, SiC thermistors have been devel-oped thanks to their ability to work in harsh environments (e.g.high temperature range) [161]–[164]. The main advantage ofSiC thermistors is the fast thermal response and the abilityto operate at high temperatures without degrading stabilityand reproducibility [159]–[164]. In addition, Wasa et al. [159]developed a highly reliable SiC thermistor with no significantageing after 2000 hours exposed to air at 400 ◦C. This SiCthermistor was also tested with 10000 cycles at a temperaturechange rate of 75 ◦C/second. In comparison to the siliconcounterpart, SiC thermistors with their excellent stability underthe impacts of the environments such as humidity and erosion,have made them an attractive candidate for temperature sens-ing in harsh environments [159]–[164].

Metal thermistors have also been developed thanks to theirhighly linear response to temperature change; hence, they aresimple in circuit design and signal measurement [5], [13].However, relatively low sensitivity limits their applica-tions. In contrast, composite mixture-based thermistors showextremely high sensitivity, which can be several orders largerthan that of the ceramic and semiconductor thermistors.These thermistors could be used for human body temper-ature detection, owing to their flexibility, stretchability andwearability. However, the material cost and the narrow work-ing temperature range are the main disadvantages of thesethermistors [81], [82]. The performance and characteristics ofthe temperature sensors are summarized in Table III.

B. Thermal Flow Sensors

Thermal flow sensors (i.e. flow sensors which measurethe velocity of surrounding fluids and the direction of fluid



TABLE III

CHARACTERISTICS OF TEMPERATURE SENSORS

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 heaterto the environment [165]. Sensitive thermoresistive elementsare commonly employed for the detection of temperaturechanges, which come from the velocity or direction changeof fluids. The working principles of three common thermalflow sensors (e.g. hot-wire/hot-film, calorimetric and timeof flight) are shown in Figure 12. The working principle,fabrication and performance of various thermal flow sensorshave been extensively reviewed [4], [5]. Table IV summarizesthe performance of various thermal flow sensors reported inliterature.

1) Hot-Wire and Hot-Film Flow Sensors: In hot-wire andhot-film configurations, a wire/film acts as both a heater anda sensor. The temperature is raised to a steady state via Jouleheating and will remain that way until a flow is applied.The cooling effect from the flow reduces the temperature andhence changes the resistance of the heater (Figure 12(a)). Thisresistance change is usually converted into a voltage changeusing a Wheatstone bridge [8], [166]–[169]. The equationgoverning the working principle of hot-wire and hot-filmthermal flow sensors is an energy balance between Jouleheating and convective cooling as follows:

RI 2 = h A (T − Te) (13)

where R, I , T and Te are the resistance of the heater, supplycurrent, temperature of heater and temperature of environment,respectively; h is the heat transfer coefficient and A is the

overall boundary area of the heater with the surroundingenvironment.

The thermoresistive effect in metals (e.g. platinum)and semiconductors (e.g. polysilicon) has been commonlyemployed for developing sensitive thermal flow sensors, sincethese materials offer high thermoresistivity (high TCRs) andproper resistivity for heating and sensing [8], [11], [169].For example, platinum has been deployed to fabricate hot-film flow sensors for measuring air velocity, which showeda high sensitivity of 0.177 mV(m/s)−1/2/mW at a powerconsumption of 45.1 mW [11]. However, these sensors havesome drawbacks in terms of working in harsh environments(e.g. high temperatures and corrosion) due to the degradationof the sensor materials. Therefore, wide band gap semiconduc-tors such as SiC have also been used to develop hot-wire/hot-film flow sensors. For example, Lyons et al. [149] developeda hot wire bridge thermal flow sensor using 3C-SiC grownon a Si substrate, in which two bridges were fabricated as aheater and a temperature sensor, and arranged in a Wheatstonebridge with two external resistors. The flow sensor showeda fast thermal time response of 3 ms, high sensitivity, highmechanical strength and a good ability to be heated to hightemperatures due to the high melting point of SiC.

2) Calorimetric Flow Sensors: Another thermal flow mech-anism is calorimetric sensing, which uses the asymmetry oftemperature profiles of upstream and downstream temperaturesensors when flow is applied (Figure 12(b)). The temperature



TABLE IV

CHARACTERISTICS OF THERMAL FLOW SENSORS

difference �T between the upstream and downstream sensingelements can be defined in the form:

�T = T(

ex1d1 − ex2d2)

(14)

where T is the heater temperature; d1 and d2 are distancesfrom the heater to the upstream and downstream resistors.Parameters x1 and x2 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 filmtechniques because it is sensitive to small flows and able todetect flow direction due to the presence of the upstreamand downstream temperature sensors. In calorimetric sens-ing, metals and semiconductors have also been commonlyused. As such, Cubukcu et al. [150] developed a germa-nium calorimetric thermal flow sensor with a high sensitivityof 232.77 V/W/(m/s), a fast thermal response of 10 ms and alow power consumption (less than 6 mW). In addition, greateffort has been paid to develop calorimetric flow sensors forhigh-temperature environments using SiC [139]. Lee et al. suc-cessfully fabricated a n-poly SiC resistive heater surroundedby one downstream and two upstream temperature sensors onsilicon nitride and silicon substrates [173]. This sensor has asensitivity of 0.73 �/sccm and a negative TCR of 1240 ppm/Kfor both heater and temperature sensors.

3) Time-of-Flight Flow Sensors: In the time of flight ther-mal sensing method, flow information is tracked by measuringthe transition time of a thermal pulse between a heater anda temperature sensor (Figure 12(c)). The transition time isdetermined based on the flow velocity, thermal conductivityand diffusivity of the fluid [4], [5].

C. Convective Inertial Sensors

1) Convective Accelerometers: The most common mechan-ical accelerometers utilize a suspended proof mass, whichgenerates displacement with applied accelerations; hence itinduces stress/strain that can be measured using piezoresistiveelements. However, mechanical accelerometers have somedrawbacks such as low shock resistance and a complex fabri-cation process. Therefore, convective accelerometers withoutany proof mass have been developed to avoid these drawbacks.The working principle of convective accelerometers was pro-posed by Weber [176], and then implemented using MEMStechnology by Leung et al. [177].

The development of convective accelerometers is based onsingle-axis (1-D), two-axes (2D) and three-axes (3D) config-urations. The working principle of convective accelerometersis shown in Fig. 13(a). Convective accelerometers operate onthe movement of a hot bubble of fluid around a heater (aself-heated resistive element by Joule heating), caused byexternal accelerations. The inertial force, when applied to themass of the hot bubble, causes asymmetry of the temperatureprofile around the heater (Figure 13(a)). This temperaturedifference is detected using two thermoresistive temperaturesensors, which are arranged at equal distances from the heater.Convective accelerometers are required for packaging in a her-metic/enclosed chamber to prevent disturbance from externalenvironments. These sensors commonly employ a cavity tothermally insulate the heater from the substrate. This helpslower the power consumption of accelerometers.

In the last 20 years, there have been a number of reports onthe development of convective accelerometers towards high



Fig. 13. Convective inertial sensors. (a) Working principle of convective accelerometers [182]. (b) Working principle of thermal gyroscopes [16].

TABLE V

THE PERFORMANCE OF INERTIAL SENSORS

sensitivity, fast response and multi-direction detection [6],[12], [152], [153], [176]–[180], [180], [181], [183]–[185]. Theperformance of various convective accelerometers is summa-rized in Table V.

As high sensitivity is desired for convective accelerom-eters, the optimization of the design parameters has beenintensively investigated. The optimization results reported byLuo et al. [179]–[181] show that an increase in the sup-ply power and cavity sizes can enhance the sensitivity ofconvective accelerometers. However, the frequency responsedecreases with increasing cavity size. Surrounding environ-ments with a low viscosity and high thermal diffusivity alsocontribute to the high sensitivity and fast frequency response of

thermal accelerometers. For example Bahari et al. [6] reportedthat a sensitivity improvement of more than 400 times couldbe made by changing the filled candidate gases from N2to C4H8.

To enable the functionality of multi-direction detection,planar convective accelerometers (2D) have been developed ona plane or thin film, which can be simply fabricated using stan-dard MEMS technologies. However, 3D accelerometers, whichare capable of measuring out-of-plane acceleration, have beensignificantly challenging to fabricate with a requirement ofvarious complex and nonstandard techniques [7]. To date, onlyNguyen et al. [12] have reported a monolithic 3-axis thermalconvective accelerometer based on the working principle of



planar accelerometers. However, the z-axis sensitivity of thissensor is relatively low, and it also requires complex additionalcircuitry for signal processing.

2) Convective Gyroscopes: It is well known that micro-gyroscopes find applications in the automotive industry suchas in anti-skid and stability control (e.g. camera and cell phonestabilization), and anti-roll applications. Gyroscopes can alsobeen found in inertial mouses and displays and other electronicdevices. Common mechanical gyroscopes use a proof masssupported by springs as a strain-induced structure, and operatebased on the Coriolis effect.

As conventional gyroscopes employ moving parts, theyare potentially fragile, and have low shock resistance andhigh levels of vibration noise. Therefore, thermal convectivegyroscopes have been proposed by Van et al. [186](Figure 13(b)). The authors proposed a dual-axis convectivemicro-gyroscope with high resolution of 0.05 deg/s, highsensitivity of 0.1mV/deg/s and bandwidth of 60 Hz at-3 dB. Since then, there have been a number of reportson the development of convective gyroscopes offering lowpower-consumption, high sensitivity and multi-directiondetection (e.g. three-dimension convective gyroscopes)[16], [186]–[190]. Table V summarizes the recent advancesin convective gyroscopes.

D. Other Thermoresistive Sensors

The thermoresistive effect has been also utilized for chem-ical composition sensing applications including gas sensors[191]–[194]. For example, in combustion a thermoresistiveelement can detect the exposure of gases on its active sur-face, due to the heat rise of combustion [192], [194]. Metaloxides and their compounds are often used for this applica-tion because they offer good catalytic properties. Platinum,palladium, and thoria compounds are also excellent catalystsfor combustion application. In addition, thermoresistors havebeen also deployed for the measurement of gas humidity [195].Furthermore, thermistors which can work in low temperatureenvironments have been used as temperature sensors to detectcryogenic liquid level [196], [197]. Finally, thermoresistors,used as a Pirani gauge heated by a Joule heating current, havebeen commonly employed for monitoring low pressure rangingfrom 0.5 to 10−4 torr [198], [199].

VI. CONCLUSION AND PERSPECTIVES

In the past few decades, the thermoresistive effect inmetals and semiconductors has been intensively investigated.The thermoresistive sensitivity of metals has been found tocommonly lie between 3,000 to 7,000 ppm/K, while thatof silicon ranges from -25,000 ppm/K to 10,000 ppm/K.Giant thermoresistive sensitivity in ceramics and other com-pounds/mixtures, which can reach up to 1012 ppm/K, hasalso been achieved. Moreover, the thermoresistive effect inwide band gap semiconductors such as silicon carbide hasbeen examined, showing their potential for operating in hightemperature environments. 3C-SiC (β − SiC) and 6H-SiC(α − SiC) have been investigated for their thermoresistiveeffects, indicating their strong feasibility for thermal sensors.

However, lowering the bulk wafer cost of (α−SiC), and grow-ing (β − SiC) thin films in a large area are both necessary forthe implementation of thermal sensors. Furthermore, impactsof growth and fabrication parameters on the thermoresistivesensitivity 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 poten-tially useful for sensors employing Joule heating effect.As such, this material can be employed for developing thermalflow sensors and convective accelerometers, which operate inhigh temperature environments. Thanks to its superior thermalcharacteristics such as high melting point, SiC could be usedin local heaters integrated within SiC systems to heat otherstructures up to high temperatures, which eliminates the useof external heaters. In addition, SiC grown on Si and subse-quently transferred onto glass by Focused Ion Beam (FIB) canavoid current leakage through the SiC/Si junction. However,for large scale production, a bonding technique is recom-mended to transfer a large-area of SiC on to glass. Therefore,SiC bonded on glass would be a suitable platform for low-costthermal sensors operating in high-temperature environments.

Recently, significant progress has been made in the fabrica-tion and characterization of MEMS thermal sensors, which uti-lize the thermoresistive effect in many metals such as platinumand semiconductors including silicon and polysilicon. Thesesensors have shown high sensitivity, linear response and lowpower consumption, which has led to their commercialization.However, the high cost and the low capability to work inhigh temperature environments are the current drawbacks.Significant development of high-temperature thermal sensorsis expected to be made in the near future, employing large bandgap semiconductors such as silicon carbide. While a numberof power electronics and circuits have been commercialized,the need for the integration of electronic circuits with thermalsensors, allowing operation at high temperatures, is expected tolead to even more development of high-temperature sensors.For this purpose, alternative thermal sensing materials withtheir high thermoresistive sensitivity need to be investigated.It is also important to develop proper packaging for thermalsensors because thermal expansion at high temperatures cancause cracking in devices.

In addition, the development of thermal sensors could bedriven towards miniaturization, a wide range of measure-ment without signal saturation, large working bandwidth andcapability of detecting multi-directions of physical signals.As such, silicon carbide and other wide band gap semicon-ductor nano-wires are also expected to be utilized in the nearfuture for integration within nanosystems operating at hightemperature conditions.

One alternative trend in the sustainable development ofthermal sensors is to investigate low-cost materials for thermalsensors, which can be processed using cleanroom-free facili-ties and user-friendly techniques, without using toxic solventsand hazardous chemicals. For example, the thermoresistiveeffect in pencil graphite has been intensively investigated,and a proof of concept of thermal flow sensors has beensuccessfully demonstrated. This indicates a possible future



development of graphite-based thermal sensors such as con-vective accelerometers. Furthermore, future techniques forimproving the adhesion of pencil graphite to a substrate, or acovering technique for protection of the graphite sensing layer,are a potential research topic towards commercializing theselow cost thermal sensors.

ACKNOWLEDGMENT

This work was performed in part at the Queensland node ofthe Australian National Fabrication Facility, a company estab-lished under the National Collaborative Research Infrastruc-ture Strategy to provide nano and micro-fabrication facilitiesfor Australia’s researchers.

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Toan Dinh received the B.Eng. and M.Sc. degreesfrom the Hanoi University of Science and Tech-nology, Vietnam, in 2009 and 2012, respectively,and the Ph.D. degree from Griffith University,in 2017. He is currently a Research Fellow withthe Queensland Micro- and Nanotechnology Center,Griffith University. His research interests includemicro/nano-electromechanical systems, physics ofsemiconductors and sensors for harsh environments,soft robotics, and advanced functional materialsfor 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, andthe Ph.D. degree from Griffith University, Australia.He is currently a Research Fellow with theQueensland Micro and Nanotechnology Center,Griffith University. His main interests focus onsilicon carbide MEMS/NEMS for applications inharsh environments. He has also been a VisitingScholar at the National Institute of AdvancedIndustrial 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 USpatents, and one book, all in micro and nanotechnologies. He was a recipientof the Japanese Government Scholarships (MEXT) for undergraduate andpostgraduate studies (2006-2013), and the GUPRS and GUIPRS scholarshipsfrom Griffith University for the doctoral course (2013-2016). He received theGU Publication Award, the GGRS-IEIS travel grant, the Springer outstandingtheses Award, and the Australian Nanotechnology Network OverseaFellowship. He was also selected to the Australian delegates to attend the23rd World Micromachines Summit in Barcelona, Spain, in 2017. He hasserved as a Reviewer for several journals, including IEEE JOURNAL OF

MICROELECTROMECHANICAL SYSTEMS, Sensors and Actuators A,Micromachines, Material Science and Engineering B, the IEEE SENSORSJOURNAL, and IEEE ELECTRON DEVICE LETTERS.

Afzaal Qamar received the M.Sc. degree in appliedphysics from the University of Engineering andTechnology, Lahore, in 2004; the M.Phil. degreein physics from the Pakistan Institute of Engineer-ing and Applied Sciences, Islamabad, in 2006, ona national competitive fellowship; and the Ph.D.degree from the Queensland Micro- and Nanotech-nology Centre, Griffith University, Australia, ona competitive international scholarship. He servedas the Manager Technical for IIIV semiconductorsdevice fabrication at the Institute of Applied Tech-

nologies from 2008 to 2014. He also served as a Research Associate atGriffith University. He is currently a Research Fellow with the Departmentof 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 ofwide bandgap semiconductors. He has authored over 35 peer-reviewed journalarticles on these areas.

Peter Woodfield received the Ph.D. degree fromSydney University, in 2001. He is currently a SeniorLecturer with the School of Engineering, GriffithUniversity, Australia. He has extensive experiencein the fields of experimental and computational heattransfer, computational fluid dynamics, thermophys-ical and transport property measurement techniques,jet impingement quench cooling, and inverse heatconduction problems.

Nam-Trung Nguyen received the Dipl.Ing.,Dr.-Ing., and Dr.-Ing. habilitation degrees fromthe Chemnitz University of Technology, Germany,in 1993, 1997, and 2004, respectively. In 1998,he was a Post-Doctoral Research Engineer at theUniversity of California at Berkeley, Berkeley,USA. From 1999 to 2013, he was an AssociateProfessor at Nanyang Technological University,Singapore. Since 2013, he has served as a Professorand the Director of the Queensland Micro- andNanotechnology Center with Griffith University,Australia.

Dzung Viet Dao received the Ph.D. degreein microelectromechanical systems (MEMS) fromRitsumeikan University, Japan, in 2003. He was atRitsumeikan University as a Post-Doctoral ResearchFellow from 2003 to 2006, a Lecturer from 2006 to2007, and the Chair Professor from 2007 to 2011.In 2011, he joined as a Senior Lecturer with theSchool of Engineering, Griffith University, where heis currently teaching in Mechatronics and Mechan-ical Engineering. He is a member of the NationalCommittee on Mechatronics, Engineers Australia.

He has authored over 280 papers in scientific journals and conferenceproceedings, and filed 15 patents. His current research interests includeSensing properties in nanostructures, MEMS sensors and actuators, siliconcarbide transducers for harsh environment, and mechatronics.

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