annealing and microstructural characterization of tin-oxide based thick film resistors

Journal of Electroceramics, 9,137-150,2002© 2003 Kluwer Academic Publishers. Manufactured in The Netherlands.

Annealing and Microstructural Characterization of Tin-Oxide BasedThick Film Resistors

KM. ANIS RAHMAN,I,*,t CHRISTOPHER J. DURNING, I SUSAN C. SCHNEIDER,2MARTIN A. SEITZ2 & WA. CHIOU3

IDepartment of Chemical Engineering and Applied Chemistry, Columbia University, New York, NY 10027, USA2Department of Electrical and Computer Engineering, Marquette University, Milwaukee, WI 53233, USA3Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208, USA

Submitted October 2,2002; Revised October 2,2002; Accepted October 17, 2002

Abstract. The sheet resistance of tin oxide based thick-film resistors exhibits two regions of temperature-dependence, described by hopping (23°C-200°C) and diffusion mechanisms (200°C-350°C), respectively.Annealing these samples causes the sheet resistance to increase in both regions. In the post-annealed samples,the hopping conduction range is extended by 50°C (23°C-250°C) while the hopping parameter, To, is decreased bymore than 50%. The activation energy of diffusion (0.60 eV) is the same for both pre- and post annealed samples, butthe magnitude of resistance in the diffusion controlled region is increased significantly as a result of annealing. Thesechanges are explained in terms of a net decrease in the concentration of tin ions in the glass matrix. From a carefulmicrostructural study it was found that a conduction path composed of tin-oxide grains or their clusters in contactwith each other does not exist in the present system. HREM micrographs showed the presence of nanocrystallinetin-oxide particles in the glass phase separating the tin-oxide grain clusters. Estimated average separation betweenthe nanocrystals in 4 nm, consistent with a variable-range hopping conduction via the dissolved tin ions in the glassmatrix.

Keywords: thick-film resistor, tin-oxide, annealing microstructure, variable-range hopping, ionic diffusion

1. Introduction

Thick-Film Resistors (TFRs) are a class or resistivematerial used in a variety of applications [1]. Thesematerials are fabricated from an "ink" that is madeby mixing a conducting phase and a dielectric phasein known proportions via an organic binder such asethylcellulose [2]. The ink is applied on an insulatingsubstrate, dried in air and the assembly is then sin-tered at temperatures well above the glass transitionpoint. The thickness of the finished resistor may varyfrom a few micrometers to hundreds of micrometers,depending on the type of application. An importantparameter that characterizes the TFRs is the sheet re-

'To whom all correspondence should be addressed.tPresent address: 2218 Southpoint Drive, Hummelstown, PA 17036,USA.

sistance [3], Ro, given by Ro = Rw/ I, where R isthe measured resistance of a resistor with width wandlength I. Many different oxides and glasses may be usedas the conducting and dielectric phases, respectively,to produce the TFRs.I For tin-oxide based TFRs2studied by impedance spectroscopy (IS) [4] it wasfound that the sheet resistance, obtained by analyzingthe impedance spectra, exhibits two regions of behav-ior over a temperature range 23°C-350°C. In region-I (23°C-200°C) conduction was explained satisfacto-rily by the variable-range hopping [5] mechanism. Athigher temperatures (region-Il, 200°C to ~350°C), theobserved behavior is consistent with an ion-exchangetype diffusion [6], with measured activation energy of0.60 ev' It is assumed that, in region-I ionic tin dis-solved in glass served as the hopping sites, while inregion-Il, higher temperatures enable these tin ions(Sn4+) to participate in ion-exchange type diffusion

138 Anis Rahman et at.

with a network forming cation of the glass matrix, suchas, Na+ [6].

In this paper we investigate the conductionmechanism of tin-oxide based TFRs by impedancespectroscopic measurements. For studying annealingcharacteristics, time-dependent AC impedance mea-surements were carried out in-situ as the samples werebeing annealed at different fixed temperatures. Sincethe composition of the TFRs contain 70-85% glass,impedance measurements were extended to study thebehavior of specimens made from 100% glass as well.A group ofTFR samples were annealed and then cooleddown to room temperature. The temperature depen-dence was then studied by a conventional DC method.

We also investigate the microstructure of these TFRs(Section 4). From a physical point of view, the con-duction processes are determined mainly by the mi-crostructure. This depends on several factors such asingredient materials, the thermodynamics of sinteringand the sintering conditions i.e., whether solid or liq-uid phase sintering took place [2]. Electron microscopywas conducted to study the local microstructure ofthe glass-grain boundary and the glassy regions thatseparate the grain-cluster regions.

2. Materials and Methods

Tin-oxide based TFRs for the present study were ob-tained from the Lapp Insulator Company, LeRoy, NY.TFRs of three different compositions designated asL70, L80 and L85 were studied, where L70 stands fora sample containing 70% glass and 30% metal-oxideby weight, and similarly for L80 and L85 samples. Themain constituents of glass are Si02 (61 %), CaO (13%),Ah03 (11%) with small amounts of Na-O (~1 %), K20(~3%), MgO (~3%) and ZnO (~4.5%). The metal-oxide was composed mainly of Sn02 with a small per-centage (~5%) of Sb20s mixed in it whose purpose isbelieved to dope the tin-oxide in-situ [7]. Despite thepresence of a small amount of antimony-oxide, thesematerials are historically known as tin-oxide basedglazes [7] or thick film resistors.

The sample geometry, configuration and theimpedance measurement setup are identical to thosedescribed elsewhere [4] and reproduced in Fig. 1, show-ing the geometry and electrode attachment scheme. Asmanufactured, the samples were in the shape of a rodof approximately I" dia. The rod shaped samples werefirst cut into disks (~0.6 em thick) and then cut into

Thick-film0"" 170 IJm

Pt Electrodes

Fig. 1. Sample geometry (not in scale) and electrode arrangement.

wedge (~1 em length) in order to attach electrodes.Ptaninum wires (3 mil dia) were attached to Au-Pd padsthat were previously sputter deposited on the resistorsurface making sure that the thickness of the resistormaterial was covered by deposited pad (see Fig. 1). Atwo-probe electrode configuration was used for bothAC and DC measurements.

To carry out time-dependent AC measurements, themeasurement cell was preheated to a given tempera-ture and held at that value until all time-dependent dataacquisition were over. Impedance data were acquiredcontinuously at fixed intervals until such time when anychanges in the consecutive spectra could not be iden-tified by visual inspection (see Fig. 2). The impedancemeasurements were repeated at various preset temper-atures; for each temperature a new sample was used.Following a similar procedure, measurements were re-peated on samples made from 100% glass, designatedas Base-Glaze (BG) samples.

At lower temperatures (<200°C) the changes in thespectra were slower, therefore, time dependent datawere acquired at an interval of an hour. At higher tem-peratures (::::200°C), however, the changes in the spec-tra were much faster, therefore, data were acquired athalf an hour intervals. All IS spectra were acquired overa frequency range of 5 Hz to 13 MHz using an auto-mated HP 4192A impedance analyzer; it took aboutone minute to acquire each individual spectrum overthe entire frequency range. At several temperatures, ISspectra were acquired for more than 300 hours. As aresult, a huge number of spectra were collected duringthe time-dependent measurements. These spectra wereanalyzed by an automated analysis algorithm [8] based

5.50 L70B: 200°C.

5.00

4.50

4.00

,-.. 3.50ab 3.00.....62.50

-s9 2.00.....•.- 1.50

1.00

0.50

Annealing and Microstructural Characterization 139

1.00 2.00O.OO+-----~----~----~----~----~----~----~--~

0.00 8.003.00 4.00 5.00s, (xl06,.o)

6.00 7.00

Fig. 2. Time-dependent variation in the impedance spectra of an L70 sample at 200°C.

on Tsai and Whitmore's prescription [9] that acceler-ated the analysis process significantly. However, thisautomated algorithm is suitable only for those spectracontaining a single prominent relaxation process, aswas the case for the present samples.

Specimens for transmission electron microscopy(TEM) were prepared by cutting a small piece of theTFR by a diamond wafering wheel. The TFR piecewas cleaned in an ultrasonic bath, dried in air, and thenmounted on a metal block with crystalbond, keepingthe glaze side in contact with the block. The substratewas removed by polishing on a coarse (200 grit) rotat-ing Buehler polisher. The thickness of the glaze wasbrought down to about 100 tim by subsequent pol-ishing with finer grits. Further polishing was done ona fine polishing cloth using syton, thereby reducingthe sample thickness to about 20 tim. The resultingfilm was then mounted on a holey Cu grid and finallythinned in an ion-milling machine to electron trans-parency. TEM specimens were studied using a HitachiH-700H 200 kV TEM and a Hitachi H-9000 300 kVhigh resolution TEM. Selected specimens were furtherexamined with a Hitachi HF-2000 cold field emissionatomic resolution electron microscope. Energy disper-sive X-ray (EDS) spectra were taken from the tin-oxideparticles as well as from the inter-cluster glass phasewith a beam probe size of approximately 3 nm.

3. Results and Discussion

3.1. Annealing Study

3.1.1. In-situ IS measurements. Time dependentvariations of the IS spectra of an L70 sample at 200°Care shown in Fig. 2. The spectra acquired for L80 andL85 samples (not shown here) also exhibited a similarpattern and a similar time-dependent changes. It is ev-ident from Fig. 2 that these spectra are predominantlycomposed of a single semi-circular arc, however, atlow frequencies, some scattered data points are presentwhich may appear as an additional relaxation process.Figure 3 exhibits an example of data fitting procedureof a spectrum at t = 30 h. The prominent semicircularsegment of this spectrum (and subsequently all others)was fitted well by the equivalent circuit shown in Fig. 4.It was found that the depression angle (e) was negativewith very small magnitude (-5° < e < 0°), indicatinga Debye-like relaxation.

We followed the algorithm ofTsai and Whitmore [9]to further analyze the spectra in the low frequency re-gion by subtracting the main equivalent circuit (Fig. 4),leaving only the low-frequency segment as the residu-als. In order to qualifying the low frequency segmentof the spectra as a "relaxation process," a relaxation-time need to be established. However, using our present

140 Anis Rahman et al.

5,-------------------------------------------~

4

L70G20030 Temp: 200°C, Bias: 0 V, Time=30h

a 3~"'0.•....2S.U~ 2~.•...

o 2 3 4 5 6 7

Fig. 3. Example of the fitting process and determination of the equivalent circuit.

Fig. 4. An equivalent circuit model of the tin oxide based TFRsamples.

analysis tool we were not able to do so. For a givenspectrum, the analysis procedure subtracts a fitted cir-cuit (e.g., Fig. 4) from the spectrum and then fittingcan be continued with the residual data to discover ad-ditional sub-circuits. The residual data of the presentsamples, however, do not exhibit a physically meaning-ful, clear-cut relaxation process. Therefore, most likelythe scattered points in the low frequency region are dueto an electrode effect whose origin is not clear at thispoint.

Similar results were obtained from fitting otherspectra acquired in these experiments; therefore, thesesamples can be represented by the equivalent circuitshown in Fig. 4. Here, the resistance R2 is assumed to bedue to the tin oxide grains; the parallel combination ofRI and CI is assumed to arise from the glassy mediumseparating the grains. An identical equivalent circuitwas also used to describe the room temperature behav-ior and the temperature dependent behavior [4] of sam-ples with identical compositions. However, while thereis no apparent time dependent change in the structure of

the equivalent ciruit, its parameters are expected to ex-hibit time dependent variations as indicated by the spec-tra in Fig. 2. From the spectra it was found that the re-sistance R2 is negligible compared to RI. From theplots of Figs. 2 and 3 it can be seen that R2 correspondsto the left intercept and RJ corresponds to the rightintercept of the spectra; hence it can be assumed thatR2 « RI. This is also consistent with the assumptionthat R2 arises from the tin-oxide grains while the glassyphase separating the grain-clusters give rise to RIand CI.

Figure 5 shows a plot of the normalized resistance,Ro(t)/ Ro(t = 0), obtained by normalizing RI at 200°Cfor an L70 sample. It can be seen from this plot thatas t increases, the Ro(t)/ Ro(t = 0) curve grows andthen tends to reach saturation. Figure 6 exhibits thetime-dependent behavior of base-glaze (BG) samples(made from 100% glass) over the temperature range200°C-291°C. The normalized resistance of the BGsamples does not exhibit any time-dependent changesat a fixed temperature as was observed for the tin-oxidecontaining TFR samples. Therefore, it may be assumedthat the time-dependent changes observed for the TFRsare due primarily to the fact that they contain metal-oxide in their composition.

Figure 7 shows plots of the normalized resistance ofL70 samples at different temperatures. It can be seenthat, the higher the temperature, the faster the growthof Ro(t)/ Ro(t = 0) and the faster the curve reachessaturation. Similar behavior was also observed for L80and L85 samples. These data (Fig. 7) were fitted by an

2.6

2.4

2.2

2S"-' 0

~ 1.8,-..•.."-'0Il::

1.6

1.4

1 .2


RD(T,I = 00)

~ RD(T,O)o

~ ..-...r,

88(II8o

IIo8o8,

o 50 100 350150 200 250 300

Fig. 5. Normalized resistance, Ro(t)/ Ro(t = 0), computed from R, values ofL70 samples at 2000e (in air).

Tim e (hour)

1.8 -r--------------------,

1.6

1.4

1.2S ~ ~ •'-6 1 M"'·'t::! .."'.rA.~,_~;.::;_tf.O":"',f.·"'"--t.-.·..~ .Il""i;~~_ ..--.;;1' ~_.v:::. .••~_'A-.:; 0.8 •• '" •••• • •• •• ••~

0.6

0.4

0.2

O~--~---~--~---~--~

• 200°C • 230·C • 263·C • 291·C

° 20 40 60 80

Time (hour)

Fig. 6. Normalized resistance, Ro(t)/ Ro(t = 0), computed fromR j values of Base-Glaze samples at different fixed temperatures(in air).

empirical relation,

Ro~~~o)IT =A(T)+B(T)exp(-t/C(T» (1)

where, A(T) is the saturation value at temperature T(in Kelvin), B(T) = 1 - A(T) and C(T) is the rate

constant of growth. It should be emphasized here thatEq. (1) is strictly an empirical relationship without anyphysical significance assigned to it. The sole use of thisequation is to compute the value of Ro(t)/ Ro(t = 0) atsaturation (t = <X). The change in resistance at a giventemperature, t>.Ro(T), was computed from

Ro(t) It>.Ro(T) = Ro(t = 0) x -- (Ohms),Ro(O) 1=00

where, Ro(t = 00) = A(T) obtained from Eq. (1).Figure 8 shows that the t>.Ro(T) data can be fit-

ted quite well up to 250°C by variable-range hoppingequation [5, 10-13] expressed as,

100

(2)

(TO)1/4

t>.Ro = t>.Ro,oexp T ' (3)

where, t>.Ro,o is a constant, and To is the variable-rangehopping parameter. Figure 8 indicates that at saturationthe resistance exhibits a variable-range hopping mech-anism. The variable-range hopping parameter, To canbe expressed as [4, 10]

(2.587)4To = 3'

N(Ep)R kB(4)


1.35 1.4

1.3 1.35

1.25 1.3

1.251.2

1.21.15

1.151.1 1.1

1.05 1.05

0 50 100 150 200 0 20 40 eo 80 100

2.2 2.6200°C

2.42

2.21.8

2

1.6 1.8

1.61.4

1.4,.-... 1.20 1.2--0~ 0 50 100 150 200 0 100 200 300 400,.-....•..--0 2.6 1.8Q:::;

2.4 1.7

2.2 1.6

2 1.51.8 1.41.6 1.31.4 1.21.2

1.1

0 50 100 15020 40 60 80

2.2 1.8

1.7287°C

Oi>~21.6

1.81.5

1.6 1.4

1.4 1.3

1.21.2

1.1

0 20 40 &0 80 10020 30 40 50 600 10

Time (hour)

Fig. 7. Normalized resistance, Ro(t)/ Ro(t = 0), computed from Rj values of L70 samples at different fixed temperatures (in air).

where, N(EF) is the density of hopping sites, EF is theFermi energy, Ris the variable-range hopping distance,and kB is the Boltzmann constant. Equation (4) indi-cates that a change in the value of To is an indicatorof the changes in physical quantities, viz., density ofhopping sites, N(EF), and the hopping distance, R. Thevalues of the variable-range hopping parameter, To, forthe three different sample compositions of the present

study were computed to be,

TO,L70 = (1.34 X 107 ± 0.52 x 105) K,

TO,L80 = (1.61 X 107 ± 0.64 x 105) K, (5)

To L85= (1.64 X 107 ± 0.63 x 105) K.

where, the subscripts L70, L80 and L85 indicate thevalue obtained for the respective group of samples. For

17.0

16.5aL85AL80

16.0 o L70

g~15.5

..515.0

14.5 -

14.0

0.200

o

0.205 0.210

T-1/4 (K-1I4)

0.215 0.220

Fig. 8. T-1/4 dependence of In(6Ro(T». The solid lines areregression lines fitted through respective data set.

pre-annealed samples, the corresponding values werereported before [4], they are:

T0,L70 = (2.7 x 107 ± 4.8 x 105) K,

TO,L80 = (3.2 X 107 ± 6.6 x 105) K, (6)

TO,L85 = (3.9 X 107 ± 6.2 x 105) K.

Comparing the values of Tos of pre-annealed [4]and post-annealed samples, it can be seen that, the Tosfor the post-annealed samples are between 50-58% ofthose obtained for the pre-annealed ones. This decreasein the value of To corresponds to an increase in thequantity N(EF)R3 [Eq. (4)]. The physical significanceof this change is discussed below.

3.1.2. Post-annealed DC measurements. The an-nealing experiments were augmented by DC measure-ments with a view to probe further the nature of changesdue to annealing. The temperature dependence of therelaxation time, reT) of these samples was reportedearlier [4]; where it was found that reT) follows thetrend of the resistance, RI (T), while the temperaturedependent change in the capacitive parameter, C 1(T)(see Fig. 4) was negligible. Figure 9 shows a plot ofIn(r) as a function of T-l/4, where presence of twotemperature dependent regions can be seen. Region Ican be fitted well by T-1/4 law, indicating a variablehopping conduction in this region. It is also evidentfrom Fig. 9 that reT) of all three compositions over-


-10.0.,--------,-----------,

-11.0

Region II

-12.0~'"6

..!:. ¢o

..5-13.0 0

.6,0 o L85o o L80.6,

-14.0 c .6, L70

1::. -VRHfit

-15.0 +-~+-'-"~+-'-"~t_'_'~t_'_'~t_'_'~t_'_'~f_"_'_-"-'-j

0.200 0.2050.210 0.2150.220 0.225 0.2300.235 0.240

T-1/4 (K.1/4)

Fig. 9. T-1/4 dependence of In(T(T» shows existence of two tem-perature dependent regions similar to Ro vs. T-1/4 data. The solidline is the VRHfit in region I (see text for explanation of overlappingdata points).

laps. This is because the relaxation time is independenton the geometry of the specimens: r = RI C 1 = pe.

It was also found that the time dependence of thenormalized relaxation time, r(t)/r(t = 0) follows ex-actly the same trend as the time dependence of the resis-tance, Ro(t)/ Ro(t = 0) (Fig. 7), while no appreciabletime dependent change was observed in the normal-ized capacitance, C1 (t)/ C1 (t = 0). Therefore, a studyof changes in resistance alone is expected to suffice toprobe the changes that occurred in the specimen as aresult of annealing.

Samples from each composition were annealed inexcess of 150 hours at a temperature between 275°C-300°C. The duration and temperature for annealingwere chosen so that the time-dependent changes in re-sistance of each sample would reach saturation. Theannealed samples were cooled to room temperatureand the resistance was then meausured as a functionof increasing temperature by a conventional two-probeDC method.

3.2. Comparison Between the Pre- andPost-annealed Samples

3.2.1. Hopping conduction in region-I. Figure 10shows a plot of the post-annealed Ro,dc(T) data


Fig. 12. An SEM micrograph of the glaze-substrate interface of thetin-oxide based TFR samples.

investigate the local microstructure of the grain bound-aries and the grain-glass interfaces. Figure 12 showsan SEM micrograph of the glaze-substrate interface;the glaze side is shown at the top. This micrographshows an overall arrangement of the tin-oxide grains,formed due to recrystallization after liquid phase sin-tering (see below), in the glass matrix. A zigzag de-marcation line can be observed between the glaze andthe porcelain substrate. It also shows that the clustersof tin-oxide grains (white specks) are randomly dis-tributed through tout the thickness of the glaze and theclusters are separated by glassy layers of varying thick-nesses. An average thickness of the glaze was estimatedto be 170 {Lm.

Figure 13 shows a representative TEM micrographof the glaze area from which it can be seen that the tinoxide grains are embedded in the glassy matrix. Fromthis and other TEM micrographs it was found that thegrain size varies between 0.1 {Lm and 0.8 {Lm, withan estimated average size of (0.36 ± 0.10) {Lm. Sincethese samples were fired at about 1200°C, liquid phasesintering is expected to have occurred. Upon cooling,the tin-oxide is expected to precipitate out and recrys-tallize. This is indeed evident from the micrograph ofFig. 13. The smooth crystal faces of the Sn02 grains(as opposed to the sharp cornered particles that usuallyresults from grinding) indicate the precipitation andgrain formation of tin-oxide during post-sinter cooling.

Fig. 13. TEM micrograph showing that tin oxide grain clusters areembedded in the glass matrix.

It can also be seen that the tin-oxide grains form clus-ters that are embeded in the glassy matrix, and glassyregions separate the clusters from one another. An av-erage thickness of the glass layers separating the tin-oxide grain clusters was estimated to be 0.4 iur: Sincetypical tunneling distance is of the order of 20 A [16] orless, a bigger intercluster separation indicates that tun-neling conduction is not likely to occur in this system.

High resolution TEM was carried out to examine(i) the interface between tin-oxide grains and glass tosee any possible structural changes that might have oc-curred in the vicinity of the tin-oxide grains by the re-action with glass ingredients during sintering, (ii) theinterfaces between tin-oxide grains in a cluster, and (iii)the local microstructure of the glass region separatingthe tin-oxide cluster. Figure 14 shows a typical inter-face between the Sn02 crystalline phase (identified bythe lattice fringes) and the amorphous glass phase. Theabsence of a sharp boundary at the interface can be ob-served, however, existence of any additional phase atthe grain-glass interface is not evident except that thelattice fringes of Sn02 extend into the glass for about1nm.

A lattice image of the grain boundary between twoSnOz grains is shown in Fig. 15. This micrograph de-picts two grains that have joined together at the latticelevel, thus indicating the existence of a continuous pathwithin the clusters. If the majority of the grains in aclus-ter are joined together at the lattice level, then the intra-cluster conduction would have a lesser or negligible


Fig. J 4. High resolution micrograph of interface between a tin oxide grain and glass phase.

Fig. J5. Lattice image showing the interface between two tin oxide grains.

electrical impedence compared to the conduction pathcomposed of glassy phase between the tin-oxide clus-ters. This was indeed observed from the impedancespectra (Fig. 2); the value of R2 was negligible com-pared to R, (Fig. 4), consequently, the glassy regionseparating the tin-oxide clusters is expected to playthe most important role in determining the conductionmechanism.

Figure 16 exhibits a high-resolution micrograph ofthe glass phase separating the tin-oxide grain clusters.The lattice fringes on the left are due to a tin-oxidegrain, while the amorphous glass phase does not ex-hibit any regular fringe pattern. However, it can be seenthat there are small crystallites (a few are indicated bythe arrow-heads) of dimension varying between 1 to2 nm, scattered in the glass phase. These nanocrys-talline particles reflect some sort of structural inho-mogeneities introduced in the glass matrix [15]. It wassuspected that these nanocrystals could form a continu-ous path in the glass phase that separates the tin-oxide

clusters. However, from a careful examination of thehigh-resolution micrographs, no evidence of a contin-uous path was found. An average distance between thenanocrystals was estimated to be 4 nm. Since typicaltunneling distance is expected to be 1-2 nm [16], there-fore, a tunneling path is most likely not present betweenthe clusters via these nanocrystals. Thus a conductionpath through the microstructure of the present TFRswould inevitably involve the inter-cluster glass phase.

The inter-planar distance the nanocrystal latticefringes (Fig. 16) matched with certain d-spacings ofSn02, e.g., (112), (202) and (220) [17]. Thus it may beassumed that at the firing temperature of about 1200°Cthe glass matrix was saturated with tin ions; duringrapid cooling after the furnace was shut off, tin-oxidehas precipitated out to form the grains and the clusters.However, the excess tin, that was not used up by thegrain formation process, have formed the nanocrystalsduring the slow cooling process, long after the furnacewas shut off.


Fig. 16. A lattice image of the glass phase separating the grains. The grain lattice (on the left) is identified by the fringes. The inter-cluster glassphase (on the right) shows presence of nano-crystalline particles (few identified by the arrow-heads).

We acquired EDS spectra (Fig. 17) from a tin-oxidegrain and glass regions of the TFR, respectively. EDSanalysis of the grain region (marked A in Fig. 13) showsa clear abundance of Sn (Fig. 17(a)) while in the glassmatrix area (marked B in Fig. 13) the major compo-

nent is Si. Thus, it is clearly seen that the grains arecomposed predominantly of Sn while the glass matrixexhibit an abundance of Si. This is consistent with theingredients used to fabricate these samples. However,while from the foregoing analysis it can reasonably be

iISn (a)I!i

I.

en

""oU (b)

o 2 4 6Energy (ke V)

8 10

Fig. 17. (a) An EDS spectrum obtained from the grain region(marked A in Fig. 12) showing an abundance of Sn, and (b) a spec-trum obtained from the glass matrix region (marked B in Fig. 12)showing an abundance of Si.

assumed that a finite concentration of tin ion has beenincorporated in glass due to liquid phase sintering, wewere not able to quantify tin ion concentration by thepresent analysis.

Inspecting Fig. 13 it can also be seen that a con-duction path composed solely of the tin-oxide grainsand/or their clusters in contact with each other doesnot exist in the present system. It has been reportedthat in RU02 based TFRs [2, 18-20], a path composedof metal-oxide grains separated by very thin layer ofglass serves as the main conduction path via a tunnelingmechanism. As an evidence of this proposition, a TEMstudy by Chiang et al. [20] indicated that the glassylayers separating the RU02 grains were only 10-13 Athick, a distance quite consistent with tunneling mech-anism. In the present tin-oxide based TFRs, however,it can be seen that the clusters of Sn02 grains are sepa-rated by much thicker regions of glass ("'0.4 j.Lm) andthe nanocrystals within these regions have an averageseparation of 4 nm.

This large separation is inconsistent with direct tun-neling of charge carriers between the clusters but is con-sistent with hopping mechanism via tin ions serving ashopping sites. According to Mott and Davis [21], Elliot


[22] and Sklovskii and Efros [10] a possible mechanismfor charge transfer through an amorphous glass is elec-tron hopping between localized states. Morgan et al.[7] And Dyshel' et al. [23,24] have pointed out that forhigh resistivity (p > 200 Qm) tin-oxide based thick-films, electron hopping may occur via the localizedstates present in the glass matrix. The present system(p ~ 1900 Qm for L70 samples) supports this hypoth-esis of electron hopping from one tin-oxide cluster toanother where tin ions in the glassy layers serve ashopping centers.

5. Conclusions

The annealing behavior in the tin oxide based TFR's ofthe present study can be described in terms of variable-range hopping and an ion exchange type diffusion, re-spectively, in the two temperature-dependent regions ofinterest. The observed increase in the sheet-resistanceas a result of annealing is due to a net decrease in theconcentration of tin ions in the glass matrix. Basedon the results of TEM analysis, it can be concludedthat a tunneling path is highly unlikely through the mi-crostructure of the present tin-oxide based TFRs. Elec-tron hopping, assisted by the localized, multivalent tinions dissolved in the glass during sintering, constitutesthe main conduction-path. The hopping path is consis-tent with Motts T-1/4 temperature dependence of theresistance.

Notes

1. It may be noted here that resistor inks comonly used in hybridmicroelectronic circuits are made from RU02 and are also calledthick film resistor. However, RU02 based TFRs are significantlydifferent from the ones being considered here; they differ in com-position, in type of glass used as well as in processing. For thisreason, one should not draw a direct comparison between thesetwo classes of TFRs.

2. Although the actual composition of the tin-oxide based TFRs con-tain small amount of antimony oxide, historically these materialsare refered to as tin-oxide based glaze or TFR.

References

1. J.E. Sergent and C.A. Harper (ed.), Hybrid MicroelectronicsHandbook, 2nd edn. (McGraw-Hill, New York, 1995); M.L.Topfer, Thick-Film Microelectronics, Fabrication, Design andApplications (Van Nostrand Reinhold, New York, 1971); M.Prudenziati (ed.), Thick Film Sensors (Elsevier, New York,


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