plasma sprayed resistors -...

Electrocomponent Science and Technology, 1980, Vol. 7, pp. 125-1290305- 3091/80/0701-0125506.50/0

(C) 1980 Gordon and Breach Science Publishers, Inc.Printed in Great Brita

PLASMA SPRAYED RESISTORS

D. P. H. SMITH and J. C. ANDERSON

Materials Section, Electrical Engineering Department, Imperial College, London SW7, 2BT, U.K..

(Received February 13, 1980)

A range of films of mixed composition, prepared by arc plasma spraying, has been investigated. Both free powderand powder in a plastic binder forming a rod have been used in the spray process. A variety of mixtures ofinsulators, metals and semiconductors has been examined and it is shown that resistivity/temperature curvesfor the specimens produced have in general two points of inflection, the temperatures of which vary withcomposition. This allows prediction of a composition giving low T.C.R. at room temperatures for any givenmetal/semiconductor combination. A qualitative theoretical model explaining this effect is presented. It has alsobeen demonstrated that a conductor/insulator combination need not necessarily exhibit a sharp transition.This allows a broad range of resistance values to be obtained simply by varying composition.

1. INTRODUCTION

The preparation of thick-film resistors by arc plasmaspraying (APS) of powders has been described inearlier papers. 1,2 The advantage of this method isthat the process is cheap and quick and the substratesused do not need to be the expensive alumina requiredby thick-film screen printing technology. In thispaper we report on an investigation aimed atestablishing the criteria for the design of APSresistors having a wide range of resistance withlow T.C.R.’s.

2. EXPERIMENTAL PROCEDURE

2.1. Spraying Procedure

All resistors have been prepared by spraying at400 A with a gas flow rate of 251 1/min using apowder feed hopper. The spraying distance was 5 cmand the substrates are rotated under the plasma on a17 cm diameter drum at 500 r,p.m. The gun istranslated during spraying at 420 cm/min. Thesubstrates were soda-glass microscope slides and abar pattern of resistors, each bar being 1.5 cm by0.3 cm, was produced by photo resist masking asdescribed in previous papers, 1,2

2.2. Resistivity- Composition

When spraying mixtures of powders of high and lowresistivity it is important to have as smooth a

125

resistivity versus composition curve as possible,with no sharp transitions in the resistivity regionsof interest. This enables the correct compositionfor a particular resistivity material to be chosenwith little error.

Theoretical considerations of this problem havein the past been based on statistically predicting theformation of discrete chains of highly conductingmaterial in an insulating matrix, whereas in practicemultiple contacts between chains are bound to exist.Scarisbricka considered the case of equal sizeconducting and insulating spheres whose size isvery much smaller than the bulk. The probability ofchain formation across a small (microscale) volumeusing a random walk is found to be

P= Vc(Vc -/) (1)

where Vc is the volume fraction of the conductingmaterial. These volumes which Scarisbrick took asspherical, are inter-connected to form a unit cube ofthe bulk material composed of multiply connectedchains. The randomly arrayed chains are thenresolved into three perpendicular directions (Cartesiancoordinates) and thus the area of contact to anyface of the unit cube is determined. This combinedwith the probability factor derived in Eq. (1) givesa resistivity corresponding to the volume fraction Vc

Pc

where Pc is the resistivity of the highly conductingspheres and C2 is the square cross-section of the

126 D.P.H. SMITH AND J. C. ANDERSON

(cm)10

10

10-

0

Exper.irnentaipoints from

--’i.-" FeO.IA2O3mixtures

Theoretical curvedue to Scarisbrick

I

\\

,l20 40 60 80 1OO

FIGURE 1 Resistivity v. volume fraction for F% O4/A12 Omixtures (1- 3 um particle size).

chains touching one face of the unit cube (which isalso a function of Vc). This curve is plotted as thedotted line in Figure 1. In the plasma sprayingprocess, the normal powder size is a distribution ofroughly spherical, 10-90/am particles and these aredelivered to the plasma gun by a gravity feed hopper.This method is unsuitable for spraying powders ofless than 5/am. Keeping the particle sizeappreciably smaller than the film thickness isnecessary to meet the requirements of the theorygiven above and the thickness of the sprayed filmsused would not allow this to be done with particlesize up to 90/am.A method of encasing fine powder in a polymer

binder and forming this as a rod, which is subsequentlyfed into the plasma flame, has been tried and hasmet with moderate success. Only fairly refractorymaterials have been sprayed by this process and thefilms exhibit poorer adhesion than their hopper-fedcounterparts. However a set ofFe3 O4/A12 O3 powders(particle size 1-3/am) has been sprayed by this

method and the resultant resistivity versuscomposition curve is shown in Figure 1. As-sprayedFe3 O4 is a low resistivity semiconductor with a lowactivation energy of 0.09 eV. The deviation of theexperimentally obtained curve from the theoreticalmay be due in part to the rather thin films(10-15/am) prepared for this study. The curveshows a higher resistivity than would be expectedfor a particular volume fraction of Fe3 O4.Scarisbrick3 predicted this behaviour as the filmthickness decreased towards a two-dimensionalfilm. Despite this, the curve does represent asmooth variation of resistivity versus composition,although only high resistances are available (> 2 kohm)with very poor T.C.R. (-12000 p.p.m.) and pooradhesion.

When the particle sizes between the conducting andinsulating phases differ, a form of threshold appears(see Figure 2). For the case of large conductingparticles and small insulating particles an increasedvolume fraction of conducting material is necessarybefore continuous chains form and when they dothe chain is of comparatively low resistivity (see

103

10z

10

--I

-I

45-9Opm Ni, 15pm A[20315-45pm Ni, 15prnA[203

1-201Jm NiO=n 20 -150i.i.rn Co0

I. ,!0 20 40 60 eo lOO

% Ni in A1203 by weight&*lo NiO in CoO by weight

FIGURE 2 Resistivity v. volume fraction formetal/insulator mixtures of unequal particle sizes.

PLASMA SPRAYED RESISTORS 127

the full curve in Figure 2). As the particle size ratioof metal to insulator is decreased to approximatelythree times, the threshold moves to a lower volumefraction with a corresponding increase in theresistivity at the threshold.

In the case of small metallic particles mixed withlarge insulating particles, the threshold occurs at avery small volume fraction and gives a highresistivity value. Subsequent increase in volumefraction of the metallic phase results in a rapiddecrease in resistivity as the fine metallic particlessurround the large insulating particles. Once thissituation has been reached and the insulating particles.have been isolated, a conducting matrixis formed and the resistivity decreases fairly uniformlywith volume fraction (see the dotted curve in Figure2). These results are not surprising as similarbehaviour has been observed elsewhere.4

In the case of a range of particle sizes for boththe conducting and insulating species, the resultingcurve is similar to the one shown for NiO/CoO inFigure 2, (NiO partially reduces to form a dispersionof Ni), i.e. for small metallic particles mixedwith large insulating ones. A set of Ni/V20s/A12 O3powders with particle sizes of 10-90/m has beensprayed and has given such a curve.

This means that normal plasma sprayed powdersare unsuitable for producing a smooth resistivity-composition curve, but if the powders are carefullysieved (or prepared) to a fairly narrow particle sizethe sharp transition from high to low resistanceover a narrow composition range can be avoided.

2.3. T. CR. of Composite Systems

The T.C.R. of a simple system such as a metal-insulator mixture (e.g. Ni-A12 03) or a semiconductor-insulator system (e.g. Fe304-A12 03) is determinedsolely by whether the threshold for continuouschains of the metal or semi-conductor has beenreached. When this situation occurs the T.C.R. ofthe system is simply that of the metal (-2400 p.p.m.)or the semiconductor (-12000 p.p.m.) as wouldbe expected.

In a more complicated system such as a metal-semiconductor mixture or a metal-semiconductor-insulator mixture the T.C.R.’s found experimentallyexhibit a range of values from zero to the valuesgiven above for the individual metal or semiconductor(see Figures 3, 4 and 5). It can also be seen that ingeneral two turning points (i.e. two points of zeroT.C.R.) are found over the measured temperaturerange. The graphs are drawn as normalised

FIGURE 3 Normalised conductivity (with respect toconductivity minimum) v. temperature for NiO/Fe Omixtures.

conductivity curves in order to show all the curvesin the same diagram. In order to understand thisbehaviour fully, a complete description of thepossible particle shapes that occur in plasma sprayedfilms as well as the particle size distribution andprobabilities of chain and near chain formation areneeded. Work is continuing along these lines, butfor a qualitative prediction of the kind of behaviourthat might be expected, let it be assumed forsimplicity that the particles are cubes of 10/amsides. The resistance of a purely metallic chain is

T’C)

FIGURE 4 Normalised conductivity (with respect toconductivity minimum) v. temperature for Ni/V= Omixtures.

128 D.P.H. SMITH AND J. C. ANDERSON

given by

R=nRrn (l+aT)where a is the T.C.R. and n is the number of cubesin one chain (this has been taken as 2500, but thevalue does not affect the argument).

Now the conductivity is given by

where is the length and a is the cross-sectional areaof the chain.

For r cubes of semiconductor in a metal chainthe resistance is given by

ETR (n-r) Rmo (1 + 7) + r Rso e

where E is the activation energy of the semiconductor.The conductivity curves for metal chains with zero,

one, three and ten semiconducting particles in themare shown in Figure 6 for E 0.09 eV, the value forFe304.

In order to obtain the total conductivity of thesystem these expressions may be added togetherand the total curve is shown in Figure 6. Thisexhibits the two turning points that occur in mostof the films experimentally. In fact this hypothesisleads to the conclusion that another minimum occursat very high temperatures, when the pure semi.conductor matrix becomes very conducting, but

9r.- METAL CHAIN

I ON S/C PARTICITHREE $/C PARTICLES

----’--TEN S/C PARTICLES_.

//..-. ’-T(K)

GU 6 uatafive mode o conductivitytemperature o a met/semconducto mtum.

this occurs at much too high a temperature to beobserved.

Figures 3 and 4 support this hypothesisqualitatively and in fact more examples of thisbehaviour have been observed but are not reportedhere. In Figure 5 the mixtureM is in fact a 60%Ni/40% V20s mixture by weight, which issubsequently mixed with A12 03. The reason for theshift in minima towards lower temperature as theproportion ofM is decreased may be assigned tothe non-linearity in the resistivity-composition curves,that is that at low compositions of Ni there is a steepdependence of resistivity on composition. TheT.C.R.’s in Figure 5 vary from 100 p.p.m, to2000 p.p.m, at room temperature, but the resistancerange is only 0.5 ohm to kohm. However thisseries has a particle size range of 10-90 #m, whichhas been concluded to be a poor choice as far asresistivity-composition is concerned.

3. DISCUSSION AND CONCLUSIONS

From the foregoing it can be deduced that APSfilms of good T.C.R. with a wide resistance rangecould be produced if certain design rules areobserved. If equal, small-sized particles (say in therange 10-15/m) of a high resistivity, low T.C.R.metal and an insulator were used a range of resistorshaving the T.C.R. of the metal could be produced.

PLASMA SPRAYED RESISTORS 129

For example, using nichrome which has a T.C.R. of180 p.p.m., resistivities up to 50 kohm/r could beobtained with film thicknesses down to 10/am. Forhigher resistivities or for lower resistivitiesrequiring a better T.C.R., a ternary metal-semiconductor-insulator system would be required.In this case the desired resistivity with a turningpoint at room temperature (for zero T.C.R.) maybe determined experimentally by an iterative method.The addition of the semiconductor to themetal/insulator mixture will give a lower T.C.R.but also reduces the resistivity. A subsequent increasein the volume fraction of insulator in order tocompensate for the lowered resistivity will thenshift the zero point of the T.C.R., so that a furtheralteration of the metal/semiconductor volumefraction ratio will have to be made, and so on.

Using a more detailed theoretical model the numberof experimental iterations could be considerablyreduced. This model is at present being developedand will be the subject of a separate paper.

ACKNOWLEDGEMENTS

One of the authors (D. P. H. Smith) acknowledges thesupport of the Science Research Council via a StudentshipAward during the work.

REFERENCES

1. R.T. Smyth, and J. C. Anderson, Electrocomp. Sci. andTechnol., 2, (1975) 135-145.

2. R.T. Smyth, D.I.C. thesis, London University (1975).3. R. M. Scarisbrick, J. Phys. D, 6 (1973) 2098.4. A. Malliaris, and D. T. Turner, J. Appl. Phys. 42, (2)

(1971) 614.

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