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Sensors and Actuators B 205 (2014) 143–150

Contents lists available at ScienceDirect

Sensors and Actuators B: Chemical

jo ur nal home page: www.elsev ier .com/ locate /snb

gold/organic semiconductor diode for ppm-level humidity sensing

aramarz Hossein-Babaei ∗, Pejman Shabanilectronic Materials Laboratory, Industrial Control Center of Excellence, Electrical Engineering Department, K. N. Toosi University of Technology, Tehran6315-1355, Iran

r t i c l e i n f o

rticle history:eceived 4 April 2014eceived in revised form 4 August 2014ccepted 20 August 2014vailable online 27 August 2014

eywords:umidity sensor2O adsorptionold nanolayerrganic semiconductor

a b s t r a c t

The cooperative electric field of surface-adsorbed polar organic molecules has been shown to con-trol charge transport in adjacent solid layers or interfaces. While the adsorption of water monomerson different metal surfaces has also been extensively investigated, the electronic implications of themechanism have not yet been explored. Here, we show that H2O molecules, selectively adsorbed ona ∼10 nm-thick gold layer deposited on a hydrophobic semiconductor, substantially change the elec-tron distribution in the gold layer, affecting the electron energy profile at the gold/semiconductorinterface and altering the current–voltage characteristics of the structure. This concept is usedfor the fabrication of a resistive humidity sensor for ppm-level hygrometry. Made by depositinggold nanolayers on an air-stable hydrophobic organic semiconductor, oxidized poly[2-methoxy-5-(2-ethylhexyloxy)-p-phenylene vinylene] (MEH-PPV), the device demonstrates high sensitivity at H2O

EH-PPVydrophobicity

concentrations as low as ∼1 ppm in air, vacuum and inert backgrounds. The presence of gasessuch as CO2 and H2 in substantial concentrations and oxygen partial pressure variations in air donot interfere with the sensing process. Unlike common Kelvin condensation-based resistive humid-ity sensors, the electrical resistance of the presented device increases upon exposure to humidatmospheres.

© 2014 Elsevier B.V. All rights reserved.

. Introduction

While detecting many volatile substances at ppm-level concen-rations is facilitated by various commercially available sensors,umidity sensing below ∼100 ppm (relative humidity 0.4% at98 K) is still a notorious technical problem [1–3]. Studies on thedsorption of polar organic molecules on metal and semiconductorurfaces [4–8] have shown that the cooperative electric field [5,9]f such surface-adsorbed molecules can control charge transportn adjacent solid layers or interfaces [5–9]. While the adsorp-ion of water monomers on different metal surfaces has also beenxtensively investigated [10–23], the mechanism has not yet beenonsidered for electronic applications.

Today, the molecular perspective of a water monomer adsorbed

n a noble metal surface is fully conceptualized [10,15–18]. Recentndings show that the interaction takes place between the 1b1olecular orbital of the H2O molecule and the metal surface, which

∗ Corresponding author. Tel.: +98 21 8873 4172; fax: +98 21 8876 8289.E-mail addresses: fhbabaei@kntu.ac.ir, fhbabaei@yahoo.com (F. Hossein-Babaei),

shabani@ee.kntu.ac.ir (P. Shabani).

ttp://dx.doi.org/10.1016/j.snb.2014.08.061925-4005/© 2014 Elsevier B.V. All rights reserved.

transfixes the molecule close to the surface with its intrinsic elec-tric dipole standing almost parallel to the surface plane [10,17,18].The asymmetric configuration of this covalent bond transfers a netnegative charge from the molecule to the metal atom [11,17]. Ona gold (1 1 1) surface, for instance, this covalent bonding holds theH2O molecule at a distance of 3.05 A from the surface with its intrin-sic dipole moment oriented at an angle of 13◦ to the metallic surface[7,14], and transfers approximately one tenth of an electron to thenearest gold surface atom [14].

It has been shown that neither the parallel and nor the nor-mal component of the intrinsic dipole of a surface adsorbed H2Omolecule can affect the electrostatic equilibrium condition in themetal a few atomic layers away from the adsorption site [15].Here, we show that the dipole moment resulting from the asym-metric adsorption bond is roughly of the same magnitude as theintrinsic dipole and is oriented almost normal to the surface plane.The selective arrangement of these dipoles on the surface of agold layer alters the mobile electron distribution within the layer’scross-section, which can be sensed at a nearby gold/semiconductor

interface. The device whose fabrication and operational character-istics are described here utilizes this concept for the electronicdetermination of the H2O concentration in the surrounding

1 ors and Actuators B 205 (2014) 143–150

aa

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wFitsnf

N

we

rtc�wTfeigt�bdAgCi�

rdbatbotidod

Fig. 1. (a) Schematic presentation of the H2O molecules adsorbed selectively atthe rough top surface of a jagged gold nanolayer deposited on a hydrophobic sub-strate. The hydrophobicity of the substrate prevents H2O molecules from diffusingto the metal/substrate interface. (b) The predicted electron population change inthe cross-section of the gold layer; much higher electron density alterations arepredicted for thinner layers with rough surfaces. (c) The predicted departure of theFermi level from its intrinsic level plotted vs. the surface densities of the adsorbedwater monomers (dashed lines) and vs. the H2O concentration in the surroundingatmosphere (solid lines).

44 F. Hossein-Babaei, P. Shabani / Sens

tmosphere by evaluating the number of the water monomersdsorbed per unit area of a gold nanolayer.

. Theory

Upon exposure to a humid atmosphere, a layer of gold depositedn a hydrophobic substrate adsorbs H2O molecules selectively onts top surface. The hydrophobicity of the substrate ensures this spa-ial selectivity on a large-area jagged gold layer as the hydrophobicorce, stretching out from the substrate surface to considerable dis-ances in atomic scale [24], would protect metal edges at the layer’spenings and micro-cracks and would prevent H2O molecules fromiffusing to the metal/substrate interface (Fig. 1a). At low humid-

ty levels, the coverage of the gold surface with the adsorbedolecules, �, is determined through the Langmuir gas adsorption

sotherm [25]. At 298 K, these calculations, given as Appendix A,esult in a simple relationship between � and H2O concentration inhe surrounding atmosphere:

= C

C + �(1)

herein C is the water concentration in ppm, and � is a constant.or the different gold layers deposited by flash-evaporation of goldn vacuum (see below), � was experimentally determined at 298 Ko be within the 250 to 350 ppm range. Assuming the surface den-ity of the adsorption sites equal to that of the surface atoms, theumber of H2O molecules on a unit area of the substrate is obtained

rom (1):

= Aeff

A

�

a2o

= Aeff

Aa2o

C

C + �

(m−2

)(2)

herein ao is the diameter of the surface metal ions and Aeff is theffective outer (top) gold surface on A (m2) of the substrate.

The charge redistribution in the cross-section of a thin gold layer,esulting from the selective adsorption of water monomers on itsop surface, is determined through the standard electrostatic cal-ulations (refer to Appendix B). The results indicate an increase ofn in the electron density from its thermal equilibrium level, no,ithin the metal beyond a nanometer below the surface (Fig. 1b).

he effect is more profound in thinner metal layers with rough sur-aces (Fig. 1b). The total density-of-state function around the Ferminergy level (EF) in gold [26] translates �n into a change in EF whichs as much as �EF in magnitude. The plots of �EF against N forold layers of different thicknesses, produced based on the calcula-ions given in Appendix C, indicate the occurrence of more profound

EF in thinner metal layers (Fig. 1c, dashed lines). The relationshipetween �EF and C, also presented in Fig. 1c (solid lines), is, then,etermined through (2) and the relationship between �EF and N.t 298 K, the predicted �EF for a rough (Aeff/A = 250) 10 nm-thickold layer at equilibrium in air containing 5 ppm of H2O is ∼5 meV.onversely, it should be possible to measure the humidity level

n the surrounding atmosphere by an experimental evaluation ofEF.The predictions of the presented theory are verified by the

esults of the experiments carried out in different conditions on theevices fabricated (see below). Of course, other types of interactionsetween H2O molecules and a gold surface there might exist (suchs those conceivable between the electric dipoles interacting elec-rostatically with the conductive plane with no charge exchange),ut the predictions based on these assumptions hardly describe thebserved change in the electronic status of the device in responseo its exposure to ppm-level humid atmospheres. Indeed, all exper-mental observations regarding the humidity sensitivity of ourevice are described by the above given theory which is based

n the modern understanding of the H2O-gold surface interactionsescribed in Section 1.

F. Hossein-Babaei, P. Shabani / Sensors and Actuators B 205 (2014) 143–150 145

Fig. 2. (a) The schematic diagram of the device structure; insets (I) and (II) are the AFM images of the top surface before and after flash gold evaporation, respectively. InsetI nstratt ized Mt ion ba

3

an5Mpura

twalagtt

I shows an Aeff /A value of ∼250 for the sensing surface. (b) Current crowding demohe interfaces 2 and 3. (c) and (d) The flat band energy-level diagrams of an Au/oxido a dry (c) or humid (d) atmosphere depicting the H2O adsorption-caused conduct

. Materials and methods

A humidity sensor is designed and fabricated, which oper-tes based on detecting the H2O molecules adsorbed on a goldanolayer deposited on a layer of oxidized poly[2-methoxy--(2-ethylhexyloxy)-p-phenylene vinylene] (MEH-PPV) [27–30].EH-PPV has been extensively studied because of its interesting

hotonic properties [29,30]. The photonic properties of MEH-PPVndergo serious instabilities upon exposure to air [30], but it hasecently been shown that a surface oxidation process, carried outt around 298 K in air, stabilizes its electrical conductivity [27].

The device, schematically shown in Fig. 2a and b, consists ofwo Au/oxidized MEH-PPV/Au diodes which are connected in seriesith their shared thin film Au electrode exposed to the open

tmosphere. The charge distribution changes in the goldayer, caused by the surface adsorption of H2O molecules,lter the current–voltage (I–V) characteristics of the two

old/semiconductor junctions. Current variations are detected athe coupled biasing and measurement circuit and translated intohe H2O concentration in the surrounding atmosphere based on

ed on the device cross-section; the humidity sensitive conduction barrier forms atEH-PPV/Au/oxidized MEH-PPV/Au structure with its central Au electrode exposedrriers (circled energy steps in (d)).

the calibration tests and the analytical relationships presented inSection 2.

MEH-PPV, a hole conducting organic semiconductor, is selectedbecause (a) it is hydrophobic [29,30] and, hence, charge transporta-tion in a layer of MEH-PPV, as well as in the device componentsburied under, is not affected by the surrounding humid atmo-sphere; (b) its highest occupied molecular orbital (HOMO) energylevel is below EF of gold [31,32] at an energy difference comparableto the predicted humidity-caused �EF in thin gold layers makingthe Au/MEH-PPV junctions suitable for �EF detection; and (c) theelectronic features of its junction with gold have been describedconsidering with low levels of interfacial traps and no “Fermi levelpining” [31,32]. The occurrence of Fermi level pining would hin-der low level humidity detection as it would conceal all Fermi levelvariation-based phenomena.

Sample devices are fabricated on 8 mm × 12 mm polyethyleneterephthalate substrates. A 100 nm-thick layer of gold is deposited

on the substrate by thermal evaporation in vacuum. The gold layeris divided into two electrodes of approximately equal size by scrap-ing off the gold in a 1.0 mm wide line across the center of the

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borur(bbuai54

iagbbSdwtwtlTf

4

ddbdbgo

46 F. Hossein-Babaei, P. Shabani / Sens

ubstrate. 20 mm long segments of fine gold wire are attached alonghe outer edges of the electrodes using conductive ink each coveringn area of ∼0.5 mm × 2 mm on the respective electrode. Poly [2-ethoxy-5-(2-ethylhexyloxy)-p-phenylene vinylene] (MEH-PPV)

owder (Aldrich 541443) is dissolved in toluene to produce solu-ions with concentration in the range of 2 to 10 mg cm−3. The entireubstrate surface is spin coated with this solution at 3000 rpm. Sam-les with different MEH-PPV layer thicknesses, 50 to 200 nm, areade using solutions of different concentrations. Undoped MEH-

PV is of low electrical conductivity, and the 1.0 mm separatedold electrodes buried under the MEH-PPV layer are electricallysolated. After drying, the coated substrate is left on a hot plate at40 K in air overnight for oxidation [27]. The surface of the oxi-ized layer as observed by atomic force microscope (Solver Next,T-MDT) is presented as inset (I) in Fig. 2a indicating almost a flat

urface in nanometric scale. The substrate is, then, placed in a vac-um chamber at 10−3 Pa to flash-evaporate the humidity sensingold layer which covers a 4 mm × 4 mm area at the center of theubstrate (Fig. 2a and b). The nominal thickness of this layer, deter-ined based on the reading of a calibrated quartz microbalance,

aries from one sample to another in the range of 7 to 100 nm. Theoughness of the surface, as observed with atomic force microscopeSolver Next, NT-MDT), also varies among the layers deposited atifferent conditions; the example given as inset (II) in Fig. 2a haseff/A value of 250.

The fabricated samples are characterized in a versatile gas cham-er at different atmospheric conditions. The operating temperaturef all samples is 298 K. The current versus voltage diagrams andesistance measurements are carried out within the gas chambersing a source measure unit (Keithley 238), while the results ofesistance measurements carried out using a portable ohmmeterSanwa PCLink-5000) are sufficient for reproducibility and repeata-ility tests. At low humidity levels, H2O concentration is calibratedased on the readings of a commercial dew point measurementnit (DewPro MMY 30). The lowest humidity level examined in airt 1 bar is 5 ppm; even lower humidity concentrations are approx-mated by lowering the chamber pressure. Humidity tests above00 ppm are calibrated using a capacitive humidity sensor (HIH-000).

After preliminary trials, 3 sample sets, each comprising 4 nom-nally similar samples, were fabricated for data collection andnalysis. The sets differed only in the nominal thickness of theold layer, measuring 10, 50, and 100 nm, respectively. Testsegan 1 week after fabrication was completed. The results (seeelow) confirmed the main predictions of our model presented inection 2. All the samples remained stable and yielded repro-ucible results as confirmed through separate retests within aeek-long period. However, response variations of up to ±35% from

he median were recorded among the nominally similar samplesithin each set. At this point, we attribute this flaw to inconsis-

encies in the thickness and roughness of the flash evaporated goldayer, though pinpointing the cause requires further investigation.he results of the most responsive sample from each set are selectedor presentation and discussion in the following section.

. Results and discussion

Since symmetric structure of the device (Fig. 2a and b) ren-ers its I–V characteristics almost insensitive to the biasing voltageirection, the device operates well with both direct and alternatingiasing types. Owing to this symmetry, the “flat band energy-level

iagram” of the device in dry atmospheres is symmetrically formedy back-to-back connection of two gold-MEH-PPV flat band dia-rams, the configuration of which is well established in the field ofptoelectronics [33–35]. The resulted diagram is shown in Fig. 2c.

d Actuators B 205 (2014) 143–150

In a humid atmosphere, the thin gold layer adsorbs H2O molecules,and this adsorption adds up an amount of �EF to the existing mis-match between the metal’s Fermi level and the semiconductor’sHOMO at the interface (Fig. 2d). Acting as a conduction barrier,this additional electron energy mismatch alters the electric cur-rent passing through the device at a constant bias. The detectedcurrent change, in turn, is translated into the variations of theequivalent resistance of the device with respect to the adsorbedH2O molecules. Considering the electron energy diagram shown inFig. 2c and d, the electrical resistance of the device, RW, is quanti-tatively related to �EF at that humidity level according to

RW = Ro exp(

�EF

kT

)+ RS (3)

wherein RS is a constant resistance accounting for the total seriesresistances, and Ro is a pre-exponential factor. At zero humidity,�EF vanishes, and results in the dry resistance as

RD = Ro + RS (4)

Hence, the predicted response levels, defined as RW/RD, fit thefollowing relationship

RW

RD= B exp

(�EF

kT

)+ D (5)

wherein B and D are fitting parameters determined by fitting of(5) to the experimentally obtained responses (see below) utilizingCurve Fitting Tool available in MATLAB. Eq. (5) relates the responsesof the device to the humidity-caused �EF in gold, which is, inturn, quantitatively connected to the H2O concentration in the sur-rounding atmosphere via the relationships presented graphicallyin Fig. 1c (solid lines).

The fabricated device operates as a resistive humidity sensorwhose resistance increases in humid atmospheres (Fig. 3a). This isopposite to the general characteristics of porous dielectric-basedresistive humidity sensors whose electrical resistances decrease inresponse to the presence of humidity. In a device made of a 10 nmgold layer, the range of measured responses, defined as RW/RD, cov-ers two orders of magnitude. The predicted RW/RD values, plottedagainst H2O concentration (Fig. 3b), fit the experimental data forrealistic values of Ro, RS, and Aeff/A. Higher sensitivities (the slopesof the profiles given in Fig. 3c) are predicted at lower humidity lev-els, and, in contrast with the characteristics of common resistivehygrometers [36,37], no lower edge is foreseen for the dynamicrange of the presented sensor.

The model-based predictions are verified by the results of mea-surements carried out at different conditions on the fabricatedsample devices (Fig. 3a–c). The observed humidity sensing capacityof the device extends well beyond the validity range of the assumedsubmonolayer Langmuir adsorption (Fig. 3b and c). This assumptionis valid for C < ∼300 ppm, but reproducible experimental responsesare recorded up to C = ∼5000 ppm in air at 298 K. We could extendthe validity of our model to higher humidity levels by assuming amultilayer adsorption [22] process and utilizing the BET [38] theoryof physical adsorption for its formulation, but this would have beenspeculative as the related literature is as yet silent about the quan-tity of the net electric charge transferred to the metal surface fromthe adsorbed H2O molecules over the first layer. The experimentalresponse levels obtained at H2O concentrations above ∼300 ppmare lower than the predicted levels implying a lower level of chargetransfer from such molecules (Fig. 3c).

The most striking technical feature of our device is the fact that,in theory, its dynamic operating range has no lower limit; and,

based on our theoretical and experimental results, we anticipatethat our sensor, structurally optimized for high sensitivity, can beutilized for sub-ppm level H2O detection. This invaluable technicalfeature of the device for ppm-level hygrometry is demonstrated in

F. Hossein-Babaei, P. Shabani / Sensors and Actuators B 205 (2014) 143–150 147

Fig. 3. The experimental verification of the predictions: (a) variations of the device resistance in response to sudden humidity changes in clean air (three cycles), aircontaminated with a trace of methanol vapor, clean air with increased oxygen partial pressure, and air containing substantial concentrations of CO2 or H2, depictingreproducible H2O sensing performance. (b) Fitting of the model-predicted (solid lines) response levels to the experimental responses (markers) of three devices withdifferent gold layer thicknesses. The dashed lines are the results of extrapolating the model predictions beyond the validity of the Langmuir isotherm; the distance occursdue to the submonolayer adsorption assumed in the calculations and the multilayer adsorption actually taking place at C > ∼300 ppm. (c) The experimental demonstrationo The es

Fnioscs

eopHtrfctmt

f the higher H2O sensitivity (slope of the curve) at lower H2O concentration levels.ample at same atmospheric conditions.

ig. 3c which indicates, in accord with the model-based predictions,o sensitivity damping down to the lowest humidity level exam-

ned. Moreover, the direction of the electrical resistance variation inur device is opposite of that in the common resistive humidity sen-ors. It is anticipated that more reliable ppm-level humidity sensingan be achieved by creating conjugated couples and coupling of theensor’s output with that of a common resistive sensor.

The responses of the device to predetermined humidity lev-ls are reproducible in clean air, air contaminated with tracesf methanol vapor, air with reduced or increased oxygen partialressure, and air containing substantial concentrations of CO2 or2 (Fig. 3a). The response time (defined as the time required for

he response to rise from the baseline to 90% of the steady stateesponse level) and recovery time (defined as the time requiredor the response to fall 90% down from its steady state level) are

onstantly 80 s and 300 s, respectively, regardless of the aforemen-ioned compositional changes in the atmosphere. The response

agnitude varies from one sample to another, which is attributedo the variations in the effective thickness and surface roughness

rror bars depicted in (b) and (c) are drawn based on the multiple readouts from the

of the top gold layer, but response adjustment for each samplerequires only a single calibration test. All the other described sens-ing features are reproducible among samples.

Another feature that sets this device apart from all other elec-tronic humidity sensors is the insensitivity of its operation to manycommon gaseous inclusions in air. As demonstrated in Fig. 3a,the presence of substantial amounts of CO2 or H2 and traces ofmethanol hardly alters the response level of the sensor to a specifiedhumidity level. Our humidity sensor is also insensitive to commonair polluting hydrocarbons, such as methane; this stems from thefact that their physisorption on gold involves no charge transfer[32]. Moreover, traces (up to 50 ppm) of ethanol, methanol, or ace-tone in air do not interfere with the sensing action (see Fig. 4), buthigh concentration of these vapors in air degrades the sensor irre-versibly. The effect of such traces in the performance of the device

at low humidity levels is demonstrated in Fig. 4.

According to the presented model and the data available,other noble metals can replace gold for the fabrication of deviceswith comparable humidity sensitivities. The interaction of silver

148 F. Hossein-Babaei, P. Shabani / Sensors an

t (s)

0

0.5

1

2.5

3

R( kΩ)

T = 298 K, d = 10 nm

1.5

2

1000 2000 3000 4000 5000 6000 70000

Clea

n ai

r with

150

ppm

hu

mid

ity

Dry clean air ( C<10 ppm)

Addi

�on

of 5

0 pp

m

Met

hano

l

3.5

Clea

n ai

r with

150

ppm

hu

mid

ity

Clea

n ai

rwith

150

ppm

hu

mid

ity

A ddi

�on

of 5

0 pp

m

Acet

one

Fig. 4. Humidity sensing at the presence of methanol and acetone traces: varia-tions of the device resistance at the stated atmospheres (red markers); blue markersdc

sgfitiusmiTewbwegts

5

tisshfirnwpcwesoaeg

epict the stability of the sensor’s baseline. (For interpretation of the references toolor in this figure legend, the reader is referred to the web version of this article.)

urface with H2O molecules, for instance, is similar to that ofold [10,17,18,20], and a slightly higher level of �EF is predictedor silver at similar conditions. In practice, however, the humid-ty sensitivity of silver-based devices, while indicating a similarrend of response variations and order of magnitude, proved to benstable and partly irreversible. This is explained in view of thenpredictable surface adsorption of oxygen species on to the silverurface at 298 K [39], which renders the H2O adsorption/desorptionechanisms complicated and irregular in air. Gold is advantageous

n this context as its surface remains oxygen-free at 298 K [40].he model also predicts the possibility of observing the describedffect in devices made by depositing gold on other air-stable,ide-bandgap, hole-conducting, hydrophobic, semiconductors of

oth organic and inorganic natures; the occurrence of the effectould depend on the relative position of the semiconductor’s Fermi

nergy level with respect to that of gold and the quality of theold/semiconductor interface. In this respect, studying the elec-ronic characteristics of gold nanolayers on hydrophobic oxideemiconductors [41] may also prove fruitful.

. Conclusions

It was shown that H2O molecules adsorbed selectively to theop surface of a gold nanolayer can cause significant changesn the mobile electron distribution at and around its bottomurface. These variations were mathematically connected to theurface density of the adsorbed H2O molecules and, hence, theumidity level at the surrounding atmosphere. Based on thesendings, a novel electronic humidity sensor was designed and fab-icated, which utilizes the exceptional electronic features of a goldanolayer/oxidized MEH-PPV junction. The operation of the deviceas described mathematically and demonstrated experimentallyroving that this humidity sensor functions best at ppm-level H2Ooncentrations. The device is affordable and easy to fabricate in aide range of sizes and shapes and is anticipated to find a vari-

ty of applications in different branches of science and technology,uch as petrochemical industries, particularly where the activityf nanoporous catalysts determines the process progress rates,

nd low loss optical fiber production units where hygrometry atxtremely low humidity levels in air, vacuum, and inert gas back-rounds is a vital necessity.

d Actuators B 205 (2014) 143–150

Appendix A.

Here, the number of H2O molecules adsorbed per unit effec-tive area of a gold thin film at equilibrium in a humid atmospherecontaining H2O at a specified concentration, C ppm, is calculated.According to the Langmuir model, the rate of gas adsorption to asolid surface is

rads = �(

1 − �)

exp(

−Eads

kBT

)P√

2� mkBT(m−2 s−1) (A.1)

wherein P is the partial pressure of H2O, Eads is the adsorptionenergy barrier, m is the molecular mass of H2O, � is the surfacecoverage, and � is the probability of adsorption at each collisionwith the surface. Considering a background atmosphere at 105 Pa,P in (A.1) is replaced by the following

P = 0.1 C(Pa) (A.2)

wherein C is the H2O concentration in the surrounding atmospherein ppm.

The desorption rate of the adsorbed molecules from the surfaceis

rdes = Kdes exp(

−Edes

kBT

)�S

(m−2 s−1

)(A.3)

where Edes is the desorption energy barrier, S is the number ofadsorption sites available per unit area of the surface, and Kdes is aproportionality constant in s−1. At equilibrium, rads = rdes, hence,

�(

1 − �)

exp(

−Eads

kBT

)0.1 C√2�mkBT

= Kdes exp(

−Edes

kBT

)�S (A.4)

resulting in

� = C

C +(

KdesS√

2�mkBT/0.1�)

exp(−(

qads/kBT)) (A.5)

wherein qads, replaced for (Edes − Eads), is the molecular adsorptionenergy. Taking the second term in the denominator of (A.5) as �results in

� = KdesS√

2�mkBT

0.1�exp(

−qads

kBT

)(A.6)

At a constant temperature, according to Eq. (A.6), � depends onthe physicochemical specifications of the adsorbing molecule andthe structure of the adsorbing surface and, hence, can be considereda constant in the framework of our calculations. Replacing Eq. (A.6)in (A.5) results in

� = C

C + �(A.7)

At C = � ppm, the surface coverage is 0.5. The numerical value of� is determined based on the experimental results. Eq. (A.7) is thestarting point of the analysis presented in Theory.

Appendix B.

Here, the magnitude of the change in the mobile charge dis-tribution in the cross-section of a gold layer, caused by a selectiveadsorption of H2O molecules on its outer (top) surface, is calculated.The adsorption of each water molecule forms a dipole perpendicu-lar to the surface with the following dipole moment (see the secondparagraph in Section 1).

Pa = 0.1e d = 4.8 × 10−30 (C × m) (A.8)

where e is 1.6 × 10−19 C, and d is the distance between the adsorbedmolecule and the surface line. The magnitude of Pa is close to that of

ors and Actuators B 205 (2014) 143–150 149

ttme

→

wtεefi

→

zar

E

u→∇

wii

�

�

td(r

A

HisaimsFtflsa

Fig. C.1. The total density-of-state function in gold plotted at the vicinity of its Fermi

[

[

[

[

[

F. Hossein-Babaei, P. Shabani / Sens

he H2O molecule’s intrinsic dipole (6.1 × 10−30 C × m). The adsorp-ion dipoles on a unit area of the gold film are numbered 1 to N. Let’s

omentarily assume zero mobile charge in the gold volume; thelectric field produced under the top gold surface, would be

E Dip = −→∇VDip = −

→∇(

14�εoεr

→r × →

P a

r3

) (V m−1

)(A.9)

herein VDip is the electric potential function around the dipole, r ishe vector defining the location in the gold layer cross-section andr is the relative permittivity of gold. The total adsorption-causedlectric field, Ea, at point r results in from the summation of theeld components generated by all dipoles:

E a =N∑

n=1

→E Dipn

(V m−1

)(A.10)

However, in reality, the electric field in the volume of the metal isero, implying that the field produced by the adsorbed molecules,s given by (A.10), is canceled out by the electric field caused byedistribution of the mobile electrons in the metal (Ered), i.e.

red + Ea = 0 (A.11)

Ered is obtained by applying the Gauss’ law to the metallic vol-me:

× →E red = �(r)

ε0εr(A.12)

herein �(r) is the charge density at point r, which can be translatednto the alteration in the number of electrons per unit volume fromts thermal equilibrium level (no), i.e.(�r) = e (n − no) = −εoεr

→∇ × →

E a

(C × m−3

)(A.13)

Replacing Ea from (A.10) in (A.13) will result in

n(�r) = 1

4�e

→∇ ×

N∑n=1

→∇(→

r × →P a

r3

)n

(m−3

)(A.14)

Eq. (A.14) relates the change in the electron density at point ro the surface density of the adsorbed H2O molecules (N) which isirectly connected to the humidity concentration (C) via (A.7). Eq.A.14) is numerically calculated for the geometry of the gold layer;esults are plotted in Fig. 1c.

ppendix C.

It is shown in Appendix B that the selective adsorption of N m−2

2O molecules to the top surface of a gold thin film causes anncrease in the mobile electron density at the vicinity of its bottomurface. Here, considering the total density-of-states, g(E), in goldt and around its Fermi energy level, this electron density increases translated into a shift of the metal’s Fermi energy level at the

etal/substrate interface. Fig. C.1, produced based on the data pre-ented in Ref. [26], shows the variations of g(E) in gold around itsermi energy level, EF1. According to (A.14) (see Appendix B), afterhe selective surface adsorption of H2O molecules to the top sur-ace, the electron population at the bottom side of the thin goldayer increases to (no + �n) m−3. The new Fermi level, EF2, is definedo that the number of states between EF1 and EF2 is sufficient forccommodating the additional �n electrons:

�n

n0=

EF2∫EF1

g (E) dE (A.15)

[

[

energy level. The numerical data are extracted from Ref. [26].

where no is the number of atoms in a unit volume, and g(E) is asgiven in Fig. C.1.

For a gold film of specified thickness and surface roughness, at astated humidity level, �n is calculated from (A.14) (see AppendixB). By replacing this value for �n in (A.15), EF2 is determined bysolving (A.15) numerically using Fig. C.1. This algorithm was usedfor calculating the magnitude of �EF = EF2 − EF1 at any H2O con-centration level. The plot of �EF against H2O concentration in thesurrounding atmosphere is given in Theory.

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Biographies

Faramarz Hossein-Babaei received the B.Sc. degree in electronic engineering fromAmir-Kabir University of Technology (Tehran Polytechnic), Iran, in 1971, and theM.Sc. degree in materials science and the Ph.D. in electrical engineering from theImperial College, London, UK, in 1975 and 1978, respectively. He is Professor of Elec-tronic Materials at the Electrical Engineering Department of K.N. Toosi University ofTechnology, Tehran, Iran. He has founded a number of hi-tech spin-off companiesmostly active in the field of high temperature materials and technology. His presentresearch interests include electric heating, microfluidics, metal oxide gas sensorsand artificial olfaction. Prof. Hossein-Babaei received the Khwarizmi InternationalAward for his outstanding R and D work on high temperature systems in 2006.

Pejman Shabani received his B.Sc. degree in electrical engineering from the Uni-versity of Tabriz, Iran, in 2000, and the M.Sc. degree in microelectronics from theIran University of Science and Technology, Tehran, Iran, in 2002. He is currently aPh.D. candidate at the Electrical Engineering Department of KNTU. His main areasof interest are organic electronics, solid state devices, and gas sensors.