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Int. J. Electron. Commun. (AEÜ)

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Regular paper

High-precision, resistor less gas pressure sensor and instrumentationamplifier in CNT technology

S. Mohammad Ali Zanjania, Massoud Doustia,⁎, Mehdi Dolatshahib

a Department of Electrical and Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, IranbDepartment of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

A R T I C L E I N F O

Keywords:Low-powerHigh precisionGas pressure sensorCNTFETInstrumentation amplifier

A B S T R A C T

In this paper, a new high-precision, pressure sensor for sensing gas molecules using a controllable voltage-modeinstrumentation amplifier (VMIA) in carbon nanotube field-effect transistor (CNTFET) technology is designed.The sensing mechanism is based on the applied force by Oxygen atoms on the surface of the carbon nanotube(CNT), which is considered as a movable electrode of sensing capacitor. The sensing mechanism is simulated inANSYS which justifies the variations of sensing capacitance, while the sensor’s output voltage is applied to anaccurate instrumentation amplifier (IA) via a switched-capacitor sensor driver. Therefore, due to the controll-ability of the transconductance and gain parameters of a CNTFET, the IA circuit provides a constant and con-trollable differential gain of up to 52 dB in a flat −3dB bandwidth of up to 3.6MHz, which provides a tunablecommon-mode rejection ratio (CMRR) of up to 121 dB in a 1.8 GHz flat, −3dB frequency bandwidth. Moreover,due to the use of the differential pair stage, the total harmonic distortion (THD) value is obtained less than0.67%. Finally, the proposed IA circuit consumes only 45.1 µW with a 22.52 nV/√Hz equivalent input referrednoise value at± 0.5 V supply.

1. Introduction

Carbon nanotubes (CNTs) with two types of single-walled (SWCNT)and multi-walled (MWCNT) are widely used in different applicationssuch as: material science, nano-mechanics and electronic engineering.This occurs due to the having of some characteristics such as: high-strength, low-density, small chip size, high stiffness, conductive andsemi-conductive modes in terms of geometric shape, unique ballisticcharacteristics, high thermal conductivity, high Young's modulus, highsensitivity to the small variations of the applied forces, emission andabsorption of light, high magnetic momentum and high mobility[1–15].

However, chirality vector (m, n) determines the angle of the Carbonatoms along the whole structure, which is classified by the wrappingmethod of Carbon sheet which results in three geometries for thecarbon nanotube. They are considered as: armchair (m, m); zigzag (m,0); and chiral (m, n). However, if k is assumed as an integer number and(m− n)= 3k; the metallic action for the SWCNT is resulted, while, itprovides semiconducting behavior for (m− n)≠ 3k [1,2].

On the other hand, in the recent years, designing high performancesensors based on CNT for monitoring Oxygen and Carbon Dioxide gasesare very challenging in many applications such as: industrial,

biomedical and environmental. So, these gas sensors should meet somespecifications including: easy configurability, low-delay responding andhigh sensitivity with good reproducibility [3].

Some examples of CNT applications to the gas detection are dis-cussed in the previously published literature [1–11], which are cate-gorized in different groups based on the changing in CNT propertieswhen exposed to the different gases. So, the use of nanotube technologyin creating pressure sensor, fluids flow and alcohol detection sensor isstudied in [4]. However, in [5] the CNT is introduced as a sensor of CO,NO and H2 gas molecules, while the application of CNT as a NH3 gassensor is expressed in [6], which is based on the reaction between CNTand NH3 gas that makes new carriers in the CNT structure. So, thesenew carriers cause some changes in the carrier concentration and theconductance of the CNT. Furthermore, the I-V characteristics of theCNT has also been used in [6], to study the effects of gas adsorption. In[9], a SWCNT is used as a mass sensor based on the axial vibration ofthe carbon nanotube. In [1], the elastic analysis of SWCNT undercombined loading in the axial direction is analyzed using ANSYS soft-ware. However, after using mesh approach and applying the relatedforces to the sensor structure, the potential energy of Carbon-Carbonbonds including torsional, bending and tensile energy of the elasticbeam is calculated using ANSYS [2].

https://doi.org/10.1016/j.aeue.2018.06.018Received 18 February 2018; Accepted 8 June 2018

⁎ Corresponding author.E-mail addresses: m_dousti@srbiau.ac.ir (M. Dousti), dolatshahi@iaun.ac.ir (M. Dolatshahi).

Int. J. Electron. Commun. (AEÜ) 93 (2018) 325–336

1434-8411/ © 2018 Elsevier GmbH. All rights reserved.

T

However, because the sensor output voltage is in the range of fewmillivolts, and due to the fact that the noise and electrode offset mayaffect the frequency spectrum, the instrumentation amplifier (IA)should be used as an essential circuit to receive high quality signalswhile, provides sufficient gain and suppressing unwanted noise andoffset [16,17]. Although, complementary metal oxide semiconductor(CMOS) amplifier was a good candidate at the front-end of these sensorsfor the past decades [16,17], but, due to the existence of limitations inthe lithographic process, short channel effects and process variationsproblems in conventional sub-micron CMOS technology [12,13].Carbon nanotube field-effect transistor (CNTFET) with MOSFET-likebehavior which provides higher mobility, quasi-ballistic transport andimproved (gm/ID) characteristics versus normalized drain current(In= ID/(W/L)), is a very good candidate to replace with CMOS circuits[12,13].

However, considering the specified chiral vector (m, n), the dia-meter of a CNT structure can be explained as it is given in Eq. (1), inwhich a=2.49 Å, is the distance between the centers of two adjacentnanotubes [12].

= + +D a m n mnπCNT

2 2

(1)

Furthermore, as it is expressed in Eq. (2), the width of the CNT (W),can be calculated using the number of CNTs in channel (N) and theinter-CNT pitch parameter (S) as follows:

= − +W N S D( 1) CNT (2)

So, the threshold voltage of a CNTFET can be simplified as it is givenin Eq. (3) [12]:

=V aVeD3T

π

CNT (3)

where e is the electric charge of an electron and Vπ=3.033 eV is theCarbon π–π bond energy.

The structural parameters of a CNTFET which are used for transistormodeling in HSPICE are summarized in Appendix A. While, theCNTFET model proposed in [12,13], is used for circuit simulations inthis paper.

On the other hand, instrumentation amplifiers have found manyapplications in medical instrumentations, electrocardiography, read-out circuit of biosensors, signal processing, high-speed signal con-ditioning, audio and video applications, monitoring and control ofbioelectronics devices specially in sub-micron analog circuits [18–29].However, the most promising properties of IAs are: variable gain ofdifferential-mode (Ad), high common-mode rejection ratio (CMRR)value, low offset value, differential to single-ended conversion, matchedinput impedance, rail-to-rail input and output swing, low noise andtotal harmonic distortion (THD) values, configurable differential gaincharacteristics and proper frequency bandwidth [16–28].

Giving the above facts, the designer should consider some importantchallenges in the design of IAs as follows:

Firstly, in order to achieve a high power efficiency, the noise valueof the IA circuit should be considered white in the required bandwidth,which results in a low amplifier’s 1/f noise corner frequency. So, theamplifier is required to have high CMRR and power supply rejectionratio (PSRR) parameter values [18].

Second, the IA should have the capability of operating in differentinput and output common-mode voltages properly.

Third, in order to maintain the system accuracy over a wide range oftemperature and due to the fact that, the sensor and the read-out cir-cuits are fabricated as a single system, the read-out circuits shouldbenefit from very low offset and gain drift values [18].

However, some IA circuits are discussed in the previously publishedliterature [16–28]. For example, a conventional IA which consists of 3op-amps and 7 resistors, suffers from the resistor mismatches, so that, ifonly 0.1% mismatch exists between the resistor ratios, a CMRR

reduction from approximately infinity to 66 dB occurs, when Ad is 0 dB[19]. However, in [17], the op-amps are built using simple two-stageamplifiers while resistors are implemented using transistors in thetriode region, but, such implementation requires 33 transistors whichdemands a large chip area while consumes 280 µW of power that is ahigh value in the recent low-power applications.

Furthermore, other previously published voltage-mode IAs (VMIAs)[16,17,20–22], suffer from the high power dissipation, low dynamicrange (DR) and require external precise resistors to change the differ-ential gain. Therefore, this makes them inappropriate for integratedcircuit implementation due to the large chip area requirement. On theother hand, current-mode IAs (CMIAs) are discussed in [23–25], thatbenefit from the use of operational transconductance amplifier (OTA) infully-differential mode which results in a reduced value for even har-monics in the output signal. Moreover, the mixed CNT-CMOS integratedsensor structure described in [11], combines CNT technology for sensorfabrication and CMOS technology for implementing programmablecurrent source and analog to digital converter (ADC) blocks. However,the programmable current source is used, due to the reduction of self-heating and also for controlling the resistance value of the CNT sensorwhich is not well controlled during fabrication.

Giving the above facts, this paper presents the design of a new high-precision gas sensor in CNT technology, which is connected to aCNTFET instrumentation amplifier to improve the circuit performances.In Section 2, the structure and functionality of a capacitive gas sensorusing a moveable electrode is described. Furthermore, the switched-capacitor sensor driver circuit as well as the sensor’s sensitivity analyzesare described in Section 3. However, in Section 4, the structure andfunction of the proposed instrumentation amplifier are discussed,while, the IA circuit simulation results in CNTFET technology are pre-sented in Section 5, where they are compared with other reported de-signs. Finally, some conclusions are presented in Section 6.

2. The proposed sensor structure

In this paper, a SWCNT is used as a clamped–free structure withattached mass for sensing gas molecules based on the method discussedin [2,9]. The role of CNT is as the top electrode in the capacitive sensorstructure, which senses the weight of the Oxygen atoms that are con-sidered as the attached masses on the surface of nanotube electrodewhile the bottom electrode designed to be fixed and air is considered asthe electrolyte.

Furthermore, the single nanotube cantilever can be fabricated overa nanometer size gap to react with gas particles (Fig. 1(a)). However, asit is shown in Fig. 1(b), when the carbon nanotube absorbs gas mole-cules, sensing electrode (top electrode) is bended and the capacitancevalue can be varied. In other words, the weight of attached masses(Oxygen atoms) on the surface of the nanotube applies a force to thestructure of top CNT electrode, which results in the displacement of thefree end of the CNT electrode that is represented by (Δd). However, theCNT displacement can be calculated using complex analytical approachfor mathematical solving of partial differential equations (PDEs) de-scribing the kinetic and dynamics of adsorption and interactions be-tween the applied force by attached Oxygen masses and displacementof CNT electrode based on the method discussed in [9]. Nevertheless,the analytical approach is very complex and a time consuming task. So,the finite-element and mesh approach can be effectively used to suc-cessfully solve the problem of interactions between the weight force ofgas molecules and displacement of the CNT’s position as it is discussedin [1,2]. Therefore, a three-dimensional beam189 element in ANSYS isused to calculate the values of bending and tensile forces. In order toproper modelling of a nanotube structure, Carbon-Carbon bonds withthe length of (a= 2.49 Å) are selected as the beam and atoms are as-sumed as the joints. Moreover, the selected nanotube is of zigzag typeand the chirality vector is assumed to be (27,0), to have the metallicrole. Fig. 2, shows the nanotube beam after considering mesh approach

S. Mohammad Ali Zanjani et al. Int. J. Electron. Commun. (AEÜ) 93 (2018) 325–336

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and placing support in one end of the beam to create clamped-freestructure as it is shown in Fig. 1(a). However, following the finite ele-ment (FE) problem-solving approach, the sensor structure can be ana-lyzed in ANSYS.

If L and ΔL are the initial length and the length variation of thenanotube structure, DCNT and t are diameter and thickness of the na-notube, then, by applying the force (F), the Young's modulus of thenanotube can be expressed as Eq. (4) [2]:

= = =Y σε

F AL L

F Lπ D t L

/Δ /

·· · ·ΔCNT (4)

2.1. Adsorption of gas molecules and interactions with CNT structure

Experimental results show that when the diameter of a nanotubevaries in the range of 0.5–1.4 nm, Young's modulus can be changed inthe range of 0.99–1.04 TPa depending on the tube type [1,2]. Never-theless, for the higher nanotube diameters, the Young's modulus re-mains almost constant [2]. According to the molar mass of Oxygenwhich is equal to 32, and considering that each mole of Oxygen hasAvogadro’s number of Oxygen atoms, the applied force at the end of thenanotube due to the absorption of each atom of Oxygen could be cal-culated. The weight of an Oxygen atom (in Newton scale) equals to:

= = × −F m g N· 5.3138492 10 ( )22 (5)

However, as described in [1,9], CNTs with different lengths, non-locality and attached mass are considered in details for each problem.However, in mass sensors, the axial vibration behavior of the SWCNTcan be used. Furthermore, using the nonlocal elasticity models, thedynamic behavior of SWCNT can be modeled. So, the mass accuracy ofthese sensors can reach to zeptograms.

The factors affecting the displacement of a nanotube under a givenapplied force, includes: length, diameter and Young's modulus of thenanotube. Considering that, SWCNT with a maximum length of 4 µmand diameter of up to 20 nm is studied in [1] and vertically alignedMWCNTs with the length of 30 µm and the diameter of 30 nm is studiedin [10], The effect of these three factors on the axial vibration ofSWCNT can be analyzed using ANSYS software. So, the analysis consistsof 3 different stages which are:

(i) Young's modulus and the diameter of the nanotube are assumed tobe 1 TPa and 5 nm, respectively and the length of the nanotube isvaried from 100 nm to 10 µm in the ANSYS simulator. So, the resultswhich are illustrated in Fig. 3, represent the maximum displacement(DMX) of the length of the nanotube (L), according to the simplifiedEq. (6). In this equation, DMX and L are scaled in nm.

= × − × + × − ×− − − −DMX L L L2.068 10 4.258 10 1.36 10 7.03 1017 3 15 2 11 9

(6)

(ii) Young's modulus and the length of the nanotube are assumed 1 TPaand 5 µm, respectively and the result of varying the diameter of thenanotube is simulated. However, Fig. 4 indicates the relationshipbetween the maximum displacement (DMX) and the diameter of thenanotube (DCNT) in the form of the simplified Eq. (7).

= × + ×− − − −DMX e e5.881 10 2.172 10D D4 1.459 5 0.463CNT CNT (7)

(iii) The Young's modulus varies based on the type of nanotube, whe-ther it is a SWCNT or MWCNT, and the mechanisms such as: theinjection of impurity ions to nanotube [2]. So, the diameter and thelength of the nanotube is assumed to be fixed of 5 nm and 5 µm,

Fig. 1. (a) Capacitive sensor structure with clamped–free SWCNT, (b) after attaching mass Mo.

Fig. 2. Mesh-based nanotube structure with onesupport and directions of the applied forces.

Fig. 3. The effect of changing the length of the nanotube from 100 nm to 10 µmon the DMX parameter.

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respectively, while, Young's modulus varies from 0.1 to 1 TPa.However, the dependency of the DMX on the Young's modulusfactor is shown in Fig. 5, while it is simplified in Eq. (8), where Yand DMX are measured by TPa and nm, respectively.

= × + ×− − − −DMX e e3.435 10 4.863 10Y Y5 6.11 6 0.7881 (8)

In order to achieve a nanotube structure with high resolution valuethat its displacement value due to the minimum applied force (i.e. theweight of Oxygen atoms) is in the picometer level, we have consideredan optimized nanotube with chirality vector (27,0) with the length,diameter and Young's modulus of 10 µm, 2.14 nm and 1 TPa, respec-tively.

By considering these values in Eqs. (6)–(8), the maximum dis-placement of the nanotube is obtained 0.382 nm for applying 1000Oxygen atoms which is illustrated in Fig. 6.

Moreover, by applying 1–10,000 Oxygen atoms to the nanotubestructure, a linear relationship between DMX and the number of Oxygenatoms is obtained, which is shown Fig. 7. However, the displacement ofCNT electrode (DMX) shows a linear behavior versus the number ofOxygen atoms (O) as it is expressed in Eq. (9).

= × + ×− −DMX O0.3821 10 7.42 103 5 (9)

2.2. Sensor capacitance calculations and variations

As it is discussed in [30], the capacitance per unit length (CP) of two

circular, parallel conducting CNT electrodes as it is shown in Fig. 1(a),with the diameter of DCNT and the distance between two centers ofnanotubes of (d) is as follows:

=⎡⎣⎢

+ − ⎤⎦⎥

=−( ) ( )

CP πε πε

ln 1 coshdD

dD

dD

0

2

0

1

CNT CNT CNT2

(10)

However, as shown in Fig. 1, the capacitor structure is composed oftwo parts, C1 with length of L1 and C2 with length of L2. It is clear that,if the number of the gas molecules increases, based on the methoddiscussed in [5], the energy levels (Fermi energy (Ef), binding energy(Eb) and energy gap (Eg) can be displaced. Therefore, for the simpli-city, it is assumed that, the maximum Oxygen atoms which are appliedto the sensor electrode in the length of 10,000 nm, are 10,000 atomswhich do not have a significant effect on the crystal structure of theCNT.

So, as it is shown in Fig. 1, assuming x=0 for the point of particleloading, it can be written that:

= − + ⇒ = −x DMXL

y d dy LDMX

dx2

2

(11)

So, the capacitance C2 for a narrow CNT bar with L2 length, is asfollows:

∫=−−

− ( )C

Ldx

cosh

d DMX

d

πεDMX

xD

22

1CNT

0

(12)

However, the total sensor capacitor for the proposed structure isobtained as follows:

= + = +C C C C L C·P1 2 1 2 (13)

For the simplicity, by the method of variation of parameters:

⎜ ⎟= ⎛⎝

⎞⎠

−u xD

coshCNT

1

(14)

In addition, by defining:

∫≜θ huu

dusinhint( ) sinθ

0 (15)

The total sensor capacitance value based on the variations of di-electric length ( dΔ ), is calculated as follows:

⎜ ⎟

⎜ ⎟

⎜ ⎟

⎜ ⎟

= + ⎡

⎣⎢

⎛⎝

⎛⎝

⎞⎠

⎞⎠

− ⎛⎝

⎛⎝

− ⎞⎠

⎞⎠

⎤

⎦⎥

−−

−

( )C πε L πε D

DMXd

D

d dD

L

coshsinhint cosh

sinhint cosh Δ

dD

CNT

CNT

CNT

0

11

0 1

12

CNT

(16)

However, as it is obvious in Fig. 8, the total sensor capacitance valueshows a linear behavior versus the displacement of dielectric length( dΔ ) for different nanotube lengths (L1).

So, in order to investigate the capacitance variations of the proposedsensor structure, due to the displacement of the CNT sensor electrode(Δd), the mesh-based, finite-element simulation results obtained fromANSYS are considered. In this way, for (Δd=0) which represents theCNT electrode condition before the gas adsorption, the sensor capaci-tance value is obtained as C0= 2.975 pF, while for the maximum dis-placement of sensor electrode (Δd= DMX=0.382 nm), the total ca-pacitance value for the sensor structure is obtained as Cmax=3.677 pF.However, the capacitance variation of the proposed sensor structure in(pF) versus the variations of Δd, in (nm) for L1=0, scale can be ex-pressed as a linear equation as follows:

= +C d1.837Δ 2.975 (17)

Giving the above facts, the capacitance value of the sensor structureincreases up to 3.677 pF for the largest displacement of CNT electrode

Fig. 4. The effect of varying the diameter of the nanotube on the maximumdisplacement parameter.

Fig. 5. The effect of Young’s modulus variations on the maximum displacementof nanotubes.

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(Δd=DMX).However, it is clear that, if the output of this sensor is connected to a

CMOS amplifier circuit, due to the larger internal capacitances of theCMOS amplifier, the output voltage of the sensor structure could not beaccurately recognizable and detectable. So, the CNTFET technology is

preferable in this case [12–15].

3. Sensor driver circuit and sensitivity analysis

3.1. Switched-Capacitor sensor driver circuit

Some efficient sensor driver circuits are discussed in the previouslypublished literature, which benefit from the standard CMOS De-SautyAC bridge [31,32] or Wheatstone bridge techniques [33,34] that useanalog interfaces for differential capacitive sensors. However, the pro-posed sensor driver circuit in this paper, benefits from the switched-capacitor (SC) technique to effectively reduce the power consumptionas well as the thermal noise value and chip size. The proposed sensordriver circuit is shown in Fig. 9. In this circuit, two non-overlap com-plementary clock signals are used which are shown in Fig. 10. Thismeans that, 0.5 μs1 and 0.5 μs2 are activated non-overlap for a durationof 200 ns and 55 ns, respectively, in a clock period of 0.5 µs. However,Ma and Mb are biased in the saturation region, while Mc is biased in thesub-threshold region and Md is biased in the linear region.

For the CNTFETs used in the driver circuit, in order to achieve agood power-delay performance, the number of nanotubes are selectedas: Na=Nc= 1, Nd=2 and Nb= 4. Then, the charging and dischar-ging resistances of the capacitive sensor are dynamically provided byMb and Md transistors, which relaxes the proposed sensor driver circuitfrom the use of extra charging/discharging passive resistors which isanother advantage of the proposed circuit.

During the 200 ns active time of 0.5 μs1, the charging path of thesensor is established and its voltage sweeps to its maximum value. On

Fig. 6. Simulation result for the displacement of top electrode DMX under 1000 Oxygen gas particles stress.

Fig. 7. The effect of variations in the number of Oxygen atoms on the DMXparameter.

Fig. 8. Total sensor capacitance value versus the displacement of the dielectriclength ( dΔ ) for different nanotube lengths (L1).

Fig. 9. The proposed switched-capacitor sensor driver circuit.

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the other hand, during the inactive time in which both 0.5 μs1 and0.5 μs2 clocks are off (that is equal to 200 ns in each period), the sen-sor’s output is connected to the input of IA stage to amplify its outputvoltage. Moreover, supplying the gate of Md transistor to the ϕ1 signal,reduces the leakage current. Then, during 55 ns active time of 0.5 μs2,the sensor is discharged through Mb transistor. In addition, the inputimpedance of the IA stage must be far greater than the channel re-sistance of Mb. Fig. 10, shows the transient response of the sensorstructure simulated in HSPICE. Moreover, the bias current of the circuitshown in Fig. 9, is 1.2 nA, which confirms the low-power performanceof the proposed circuit.

3.2. Sensor sensitivity analysis

As it is previously discussed in [35,36], one of the main perfor-mance measures of a sensor system is the sensitivity (S) of the sensor tothe physical variables which is defined as the ratio of the output voltagevariations over the displacement variations of the CNT electrode ( dΔ ).

= ∂∂

S vdΔ

out(18)

However, the simulation results indicate that, due to the capaci-tance variations in the range of 2.975–3.677 pF, the sensor’s outputvoltage can be changed in the range of 1–1.34mV. So, the displacementdependent output voltage of the sensor circuit can be expressed asfollows:

= +V d1.837Δ 2.975C (19)

where VC is in (mV) and dΔ measured in (nm) scale.Therefore, as it is shown in Fig. 11 and considering Eq. (19), it is

clear that the sensitivity value of the proposed sensor circuit to thedisplacement value of the CNT electrode due to the adsorption ofOxygen gas masses can be calculated as follows:

= =Sμ

1.837 mVnm

1.837 Vm (20)

Furthermore, as it is discussed in [35], the resolution of the pro-posed sensor circuit is defined as follows:

=→

−

−Res

vS

limv v

out p p,

out p p n, (21)

However, considering the sensitivity value calculated in Eq. (20),and due to the fact that, the equivalent input referred noise of theproposed sensor circuit at 2MHz, is obtained as 0.32 nV/ Hz , the re-solution value for the proposed sensor is calculated asRes =0.509 pm.

4. The proposed instrumentation amplifier structure

In order to reduce the effects of unwanted common-mode signals,

even harmonics and noises against the low value of differential signals,the differential amplifier structure can be used. In addition, the cross-coupling technique can be used to generate the negative output im-pedance and improve the linearity of the output signal. However, thenegative load technique is properly improves the differential gain,especially for low voltage applications. Hence, assuming that the circuitis symmetrical and matched, the instrumental amplifier which uses only7 transistors is proposed based on the approach discussed in [26,27]and shown in Fig. 12.

By considering the differential mode half-circuit, it is obvious that:

= = −−

+−A

vv

g g r r r( || || || )dout

in D Mm m ds ds ds

, . .1 5

11 3 5

(22)

So, M1 to M4 form an amplifier with the positive feedback loop, inwhich the feedback factor (ß) and differential gain (A )df are equal to:

= =gg

ß g

g

m

m

1

13

1

m

m

1

3 (23)

Fig. 10. The non-overlap complementary clock signals and the sensor’s outputvoltage.

Fig. 11. Sensitivity variations versus changing the displacement of CNT elec-trode (Δd).

VDD

Vb

Vin-Vin+

VSS

Mtail

M1 M2

M3 M4M5 M6

Vout - Vout+

Fig. 12. CNTFET-based instrumentation amplifier circuit.

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=−

=−−

−

−A AA

g g r r rg g r r r1 ß

( || || || )1 ( || || || )df

d

d

m m ds ds ds

m m ds ds ds

1 51

1 3 5

3 51

1 3 5 (24)

So, by neglecting the parallel effect of the drain-source resistancesagainst the −gm5

1, it is obtained that:

=−−

=−

−

−

−Ag gg g

gg g

( )1 ( )df

m m

m m

m

m m

1 51

3 51

1

5 3 (25)

In a similar method, considering half-circuit in common-mode andassuming that gmt is the transconductance of the tail transistor inFig. 12, it is obtained that:

= =−

+

−

+

−

−Av

vg g r r r

g g( || || || )1 (2 )c

out

in C M

m m ds ds ds

m mt, . .

1 51

1 3 5

11 (26)

=−

=−

− +

−

− −A AA

g g r r rg g r r r g g1 ß

( || || || )1 ( || || || ) (2 )cf

c

c

m m ds ds ds

m m ds ds ds m mt

1 51

1 3 5

3 51

1 3 5 11 (27)

So, by neglecting the parallel effect of the drain-source resistancesagainstgm5 , it is obtained that:

=−

− +=

− −

−

− −Ag g

g g g gg

g g

( )1 ( ) (2 )cf

m m

m m m mt

m

m mg g

g

1 51

3 51

11

1

3 52 m m

mt

1 5(28)

By combining Eqs. (25) and (28), it is resulted that:

= +−

CMRRg g

g g g1

2( )

m m

mt m m

1 5

5 3 (29)

However, according to Eqs. (25) and (29), to avoid the gain andCMRR becoming infinity, the reliable difference between gm5 and gm3should be set [26,27].

Giving the above facts, the requirements in designing a proper in-strumental amplifier in CNTFET technology includes:

(1) Since, the maximum output voltage of the sensor structure is1.34mV and a± 0.5 V supply is used for low voltage applications,so, the maximum output swing is set to be less than 450mV, so, thedifferential gain of the IA should be set below 50.2 dB. In addition,the dc offset of the output node should be below 10mV while, theCMRR value should be at least two times greater than the differ-ential gain which means to be at least 85 dB.

(2) Considering the sampling frequency of 2MHz, the cutoff frequencyof the instrumentation amplifier should be greater than the sam-pling frequency value.

(3) The input impedance of the IA circuit should be much greater thanthe channel resistor of Mb, to guarantee that the capacitor of thesensor shown in Fig. 9, does not discharge to the IA’s input im-pedance at the active phase of 0.5 μs2.

(4) According to Eq. (3), the threshold voltage is obtained asVT= 0.196 V. However, to effectively reduce the power consump-tion of the circuit, the tail transistor should be preferably biased inthe sub-threshold region.

However, to increase the transconductance of each transistor, thechannel width should be increased. But, it also increases the parasiticcapacitances as well as the power consumption. So, to achieve the bestcircuit performances, the chirality vector is set to (28,0) for transistorsand the number of nanotubes are considered as: N1=N2=16,N3=N4=N5=N6=1 and Ntail = 30 while, the centers distance ofthe two adjacent nanotubes are considered as: S1= S2= 10 nm andS3= S4=S5= S6= Stail = 20 nm.

5. Simulation results

Fig. 13 shows the frequency response for the differential gain of theproposed IA circuit assuming Vb= 0.3 V, which indicates a constantgain value of 42.5 dB up to 3.62MHz cutoff frequency.

Fig. 13. Frequency response of the differential-mode gain for the proposed IA (Vb= 0.3 V).

Fig. 14. Common mode rejection ratio (CMRR) performance of the proposed IA (Vb= 0.3 V).

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Fig. 15. Frequency performance of differential-mode gain for different values of Vb.

Fig. 16. CMRR frequency performance for different values of Vb.

Fig. 17. CMRR variations for different temperatures (Vb=0.3 V).

Fig. 18. Step response simulation result for the proposed IA circuit.

Fig. 19. Transient response of the proposed IA circuit at in differential-modewith a 10 kHz sinusoidal input signal.

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Furthermore, Fig. 14 shows the frequency response of the common-mode rejection ratio (CMRR) parameter for Vb=0.3 V, that indicates aconstant CMRR of 86.2 dB up to 1.8 GHz corner frequency. On the otherhand, in Fig. 15, the frequency responses of the differential gain para-meter for various Vb values are illustrated, so that the tail transistor canbe biased in the range of saturation to sub-threshold and the differentialgain is controllable in the range of 21.7–52.25 dB. Similarly, the CMRRadjustment in the range of 54.7–121.8 dB is illustrated in Fig. 16.Moreover, the CMRR variations for different temperatures at Vb= 0.3 Vare illustrated in Fig. 17. It is clear that, the differential gain reduces byan increase in the operating temperature.

However, HSPICE simulations show that the power consumptionof the proposed IA circuit is obtained as 45.1 µW. In addition, theinput impedance of the proposed IA is obtained as 1 TΩ up to 3 KHzfrequency and it becomes ten times smaller by every decade in-crease in the frequency, which justifies the capacitive behavior ofthe circuit of Fig. 12. Furthermore, analyzes at various frequenciesin the range of 1 KHz–10 MHz reveal the THD parameter varies inthe range of 0.58–0.67%. Moreover, at frequencies from 100 Hz to100 GHz, the equivalent input referred noise value is obtained as

22.52 nV/ Hz .Moreover, Fig. 18 shows the step response, transient simulation

result for the proposed IA circuit. Fig. 19, indicates that for an inputvoltage swing of ± 1.6 mVpp, the differential output voltage varies inthe range of ± 223mVpp. Moreover, by proper selecting of thenumber of nanotubes and pitch distances, the acceptable output dcoffset voltage is obtained 1.52 mV. In addition, Fig. 20 shows theinput and output transient responses of the proposed IA circuit afterconnecting the sensor's driver and read-out circuits to the core of IAcircuit.

Table 1, compares the performances of the proposed CNTFET-IAcircuit with its 32 nm CMOS counterpart for the same power supply andload capacitor values. The simulation results show that the importantperformance parameters such as: DC offset, Ad, CMRR, PSRR, THD andSR, are significantly improved due to the use of CNTFET technology,except for power consumption performance. However, in order toperform a fair comparison between the same IA circuits in CNT andCMOS technologies, two different small and large signal figures of merit(FOM) are defined to effectively compare both small and large signalperformance measures based on the method discussed in [31]. In such a

Fig. 20. Output voltage of the sensor (top) which is applied to IA and output voltage of IA circuit (bottom).

Table 1Comparison between the proposed VMIA in CMOS and CNTFET technologies.

Technology 32 nm CMOS 32 nm CNTFET

Aspect Ratio W1/L1=W2/L2=32 nm/100 nm N1=N2=16, S1= S2= 10 nmW3/L3=W4/L4=50 nm/130 nm N3=N4=N5=N6=1W5/L5=W6/L6=50 nm/90 nm S3= S4= S5= S6= 20 nmWtail/Ltail =W6/L6= 400m/1 µm Ntail = 3, Stail = 20 nm

Power Supply/Vb/load Capacitors ± 0.5 V/0 V/1 pF ±0.5 V/0.3 V/1 pFDifferential amp (Ad) 25.3 dB 42.5 dB−3dB BW Ad 385.3 KHz 3.62MHz0 dB BW (fT) 6.9 MHz 491MHzCMRR 31 dB 86.2 dB−3dB BW CMRR 402 KHz 1.8 GHzPhase Margin 76 °Â 90 °ÂPLOSS 15.57μW 45.1 µWOutput dc offset 4.16mV 1.52mVTHD 3.14% ≤ 0.67%Input referred noise @f= 2MHz 107 nV/ Hz 22.52 nV/ HzOutput referred noise @f= 2MHz 367 nV/ Hz consist of: 4.91 nV/ Hz consist of:

355 nV/ Hz for Flicker noise 4.14 nV/ Hz for Ficker noise

89 nV/ Hz for thermal noise and 731 pV/ Hz for thermal noise17.3 nV/ Hz for shot noise and 2.53 nV/ Hz for shot noise

PSRR+, PSRR- 27.5 dB, 26.5 dB 55.5 dB, 59.8 dBSR+, SR- 5 V/μS 61.5 V/μS, 64.86 V/μSFOMS 443MHz·pF/mW 10,886MHz·pF/mWFOML 321 (V/μS)·pF/mW 1400 (V/μS)·pF/mW

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way, for small signal conditions, the small signal (FOMS) is defined asfollows:

=FOM GBW CPower

·S

L(30)

While, for the large signal conditions, the large signal (FOML)parameter is defined as:

=FOM SR CPower

·L

L(31)

Therefore, Table 1 shows that FOMS value for the CNTFET-IA, is24.5 times greater than of that obtained for the CMOS-IA, while, theFOML value for the CNTFET-IA, is 4.36 times greater than of the FOMLvalue which is obtained for the CMOS-IA; for the same power supply,bias voltages and load capacitance conditions.

Moreover, in order to investigate the noise performance of theproposed IA circuit, the noise analyzes are performed in HSPICE.However, as it is discussed in [37,38], the Flicker and shot noises arethe dominant intrinsic noise mechanisms in the CNTFET structure. Inother words, the Flicker noise is more relevant to the lower frequencyranges, while the shot noise is more relevant to the higher frequencybands. On the other hand, regarding to the thermal noise, it is evidentthat the contributions of the drain, gate and source resistors are neg-ligible, while as it is discussed in [12–15] the capacitive behavior ofthese terminals is dominant. Therefore, the value of thermal noise inCNTFET structures is significantly smaller than the values of shot andFlicker noises. So, as it is obvious in Table 1, HSPICE simulation resultsshow that the value of the output referred noise at 2MHz frequency forCMOS IA circuit is 367 nV/ Hzwhich consist of 355 nV/ Hz Flickernoise and 89 nV/ Hz thermal noise while, it contains 17.3 nV/ Hzshot noise value.

While, the output referred noise value for the CNTFET IA circuit at2MHz frequency is 4.91 nV/ Hz consisting of 4.14 nV/ HzFlickernoise, 731 pV/ Hz thermal noise and 2.53 nV/ Hz shot noise, thatjustifies the higher contributions of Flicker and shot noises in compar-ison with the thermal noise value.

Furthermore, Table 2 compares the performances of the proposedVMIA with other related works. The results indicate that, a significantimprovement for all the performance parameters is obtained due to theuse of a low power, low voltage (LP/LV) CNTFET IA circuit whichconsists of only 7 transistors for the active area of less than 0.012 μm2.

6. Conclusions

In this paper, a highly accurate gas pressure sensor with a driver andread-out circuit in addition to an instrumentation amplifier are de-signed in 32 nm CNTFET technology, while their performances are si-mulated in ANSYS and HSPICE. This circuit can be used in variousapplications such as: robotics, e-skin and prosthetics (artificial limbs)because of the following specifications: low supply voltage, resistor-lessstructure, low-power consumption, small chip size, flat differential gainin the required frequency bandwidth, very large CMRR which is fixed ina large frequency range, good noise and harmonics performances forthe output signal and electronic adjustability.

Table2

Com

parisonbe

tweenthepe

rforman

cesof

theprop

osed

VMIA

andothe

rrepo

rted

design

s.

Referen

ceTh

isWork

2820

2324

1625

1721

22

Tech

nology

/Year

32nm

CNTF

ET18

0nm

CMOS/

2018

180nm

CMOS/

2018

180nm

CMOS/

2017

180nm

CMOS/

2016

180nm

CMOS/

2016

180nm

CMOS/

2013

500nm

CMOS/

2011

180nm

CMOS/

2007

800nm

CMOS/

2007

Power

supp

ly(V

)±0.5

±0.9

2±0.9

±0.9

3.3

±0.8

–1.8

1.7–

3.3

Ad(dB)

21.7–5

2.2

3–18

406.9–

25(vo/i d)<

100

59.5

19.5–3

2.5

4539

.96

≥40

CMRR(dB)

54.7–1

2151

120

36–5

4.2

4011

091

7516

7>

80−

3dBBW

Ad

3.62

MHz

3–14

.8MHz

2KHz

1.8–

19.3

MHz

–0.12

5–50

0KHz

10.2–1

6.8MHz

5.8KHz

–12

0Hz

−3d

BBW

CMRR

1800

MHz

68KHz

–35

9–38

3MHz

4.2MHz

>20

0Hz

10.18MHz

––

–Po

wer

dissipation(μ

W)

45.1

846

121.6

760

494

250

219–

446

280

3208

2TH

D≤

0.67

%0.

52%

−64

dB1.7%

≤4.

5%≤

3.7%

––

–Noof

active

elem

ents

7MOSF

ET2COA+

2MOSF

ET22

MOSF

ET2C

OA

8MOSF

ET>4G

mbloc

k17

MOSF

ET33

MOSF

ET73

MOSF

ET–

Noof

resistors

01

22

03

00

2–

Electron

ictuning

√√

X√

√X

√X

––

Inpu

t/ou

tput

sign

als

V/V

I/I

V/V

I/I

I/I

V/V

I/I

V/V

V/V

V/V

Inpu

treferred

noise

22.52nV

/H

z–

0.78

µW12

pA/

Hz

1.9pA

/H

z18

nV/

Hz

–22

nV/

Hz

55.59nV

/H

z10

0nV

/H

z

S. Mohammad Ali Zanjani et al. Int. J. Electron. Commun. (AEÜ) 93 (2018) 325–336

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Appendix A. CNTFET structural parameters used for circuit simulations [39]

Design parameter Symbol Value

Physical Chanel length Lch 32 nmThe length of doped CNT source/drain extension region Lss (Ldd) 32 nmThe mean free path in intrinsic CNT channel (due to non-ideal elastic scattering) Lgeff 200 nmThe width of metal gate (Sub-lithographic pitch) Wgate 6.4 nmThe thickness of high-k top (planer) gate dielectric material (HfO2) Tox 4 nmDiameter of CNT DCNT 2.72 nmThe optical phonon backscattering mean-free-path in metallic CNTs λop 15 nmThe acoustic phonon backscattering mean-free-path in metallic CNTs λap 500 nmThe distance between the centers of two adjacent CNTs Pitch= S variableCNT work function φs 4.5 eVThe Fermi level of the doped source/drain tube Efi 0.6 eVThe chirality vector of tubes (m, n) (28,0)The number of tubes in the device N variableThe dielectric constant of high-k top (planer) gate dielectric material (HfO2) Kgate 16

Appendix B. Supplementary material

Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.aeue.2018.06.018.

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