Thin Solid Films, 41 (1977) 105-111 © Elsevier Sequoia S.A., Lausanne--Printed in the Netherlands 105

ELECTRICAL RESISTIVITY AND T E M P E R A T U R E CO EF F ICIEN T OF RESISTIVITY IN G O L D - C O P P E R FILMS

A. K. PAL, P. SEN AND A. K. BARUA

Department of General Physics and X-rays, Indian Association for the Cultivation of Science, Calcutta- 700032 (India)

S. K. SHARMA

National Physical Laboratory, New Delhi (India) (Received July 12, 1976; accepted July 26, 1976)

In situ measurements were carried out in order to study the electrical behaviour of gold-copper films (300-3000 /~) of various compositions in the temperature range 30-150 °C. The experimental observations were correlated with the structural information obtained from an electron microscope study.

1. INTRODUCTION

The effect of alloying is to introduce foreign impurity atoms into the lattice; this results in a modification of the transport properties of both the solute and the solvent atoms to a degree depending on the severity of the experimental process. Alloys can be classified into two main classes: (1) homogeneous (one-phase systems) and (2) eutectic (two-phase systems). In the former the concentration of each component is constant throughout the alloy, whereas in the latter there are small crystals. Some of these contain more of one component and some contain more of the other. Such eutectics are formed when the mutual solubility of the components of the alloy is limited and the concentration of the given alloy is beyond the solubility limit.

In general, alloys are remarkable for their very high resistivities, which at first sight appear to be out of all proportion to the relative amounts of the constituent atoms. Consequently, in all alloys except dilute ones, the temperature-dependent component of the resistivity (the phonon part p~) is of lesser importance than the residual resistivity Po. Disregarding certain obvious exceptions (i.e. magnetic alloys) Matthiessen's rule holds good for dilute alloys and only begins to fail when the concentration of the second component is large enough to make the residual resistivity more than a small fraction of p~ or when there is a considerable size or valence difference between the solute and the solvent atoms. In non-dilute alloys, cases of complete miscibility for all compositions, as in the case of the Cu-Au system, are exceptions rather than the rule, most systems being restricted in their range of solid solubility. When an alloy is not a solid solution but consists of a mixture of individual crystallites each composed wholly of one component or the other, the resulting total resistivity is lower if the two components are mutually soluble. By contrast the mixed atoms of a disordered solid solution are distributed at random over all the lattice points of the sample, the periodic potential of the pure metal is bodily disrupted, and the resulting resistivity of the alloy shows a

106 A.K. PAL et al.

characteristic maximum in its dependence on concentration because of the mismatch in the atomic volumes. The influence of the atomic volumes on scattering may be rendered very much less effective by arranging the atoms into an interpenetrating superlattice using suitable techniques 1. Generally, the ordering or formation of superlattices is accompanied by a sharp fall in resistivity with minima at specific concentrations at which the superlattice has actually formed. Thus a common method of studying the order-disorder transition in alloys is to measure the change in electrical resistivity accompanying it.

The order-disorder transition has been extensively studied in bulk Cu-Au alloys 2-s. It was generally observed that the order has a maximum effect at the critical compositions AuCu3 and AuCu. For these compositions the resistivities are as low as those for the pure components.

However, there seem to be no reliable data on CuAu alloy films. We report here in situ measurements at temperatures from 30 °C to 150 °C of the resistivities of Cu-Au alloy films (300-3000 A) of various atomic compositions deposited at 150 °C. The effect of ordering was studied by measuring the change in resistivity accompanying ordering.

2. EXPERIMENTAL

Gold--copper alloys (99.999 ~o, Johnson and Matthey Co., U.K.) were flash evaporated from a molybdenum boat at a pressure of 10 - 6 Torr onto a clean 9 glass substrate. The charge, in the form of fine powder, was sprinkled over the hot molybdenum boat at a controlled rate by a mechanical vibrator so that accumu- lation of excess charge on the boat was practically avoided. If the temperature of the boat is too high, many of the particles may be blown off from the boat without evaporation. The evaporation was never continuous in spite of the extreme care taken to control the deposition parameters. However, an average rate of deposition (5-10 A s- 1) as determined by a quartz crystal oscillator could be maintained with a little effort. The temperature of the substrate was controlled by an electronic on/off temperature controller to an accuracy of + 0.5 °C. The actual temperature of the film was measured by a thermocouple placed on the substrate. The maximum rise in substrate temperature during the deposition of the thickest film was 10 °C. The thicknesses of the films were determined with a multiple-beam interferometer. The resistivities were measured in situ using the four-probe method of van der Pauw 1°.

3. RESULTS AND DISCUSSION

The results for the thickness dependence of the resistivity of Au-Cu films deposited at 150 °C are shown in Fig. 1. The thickness dependence was studied at temperatures between 30°C and 150°C. Figure 2 shows the variation of the resistivity of some Au-Cu films (500 A, 1000 A and 2000 A) with composition. The resistivity-composition curves bear a striking resemblance to observations made of bulk gold-copper alloy by Johansson and Linde 1. There is a minimum in the resistivity at the compositions where an ordered arrangement of the atoms is possible. Deposition at 150 °C, which seems to be high enough to permit atomic interchange, is expected to produce an ordered arrangement of the atoms

Au-Cu FILMS 107

t51

:30

20

a -- 30°C • - - 90°C O-- lso°c

I

~k .E

500 I I I

1000 i 500 2000 t ( thickness) in ~

2500

~L I ~" } 35 a t%Au

4 4 30°C ,--j. eOeC o ~ 150°C

I 500

I 1 I 1000 1500 2 0 0 0

t ( thickness) in A ~, 2500 3000

30

2O

E (J

~L ,c

% lO

-- 30°C , - - gO°C

O--150°C

at ,/. ~ - - J Au

~ _ ~ ' ~ } s2 ,, ./.Ao

0 I I I I 0 500 I000 1500 2000

t (thr'ckness) in A - - ~ 25000

Fig. 1. The resistivity of Au-Cu alloys of different thicknesses at temperatures of 30 °C, 90°C and 150°C.

108 A.K. PAL et al.

f E ta

A I \

l I II\ i I \\\ 2C ~ t

/ 1 / x I o / ~, x, / // % ,

~ Ii I / \ ~\ / [I ",~, \ \

f " I \ \ i I / O.\ \ . c a I i \ \ / I / 2OOOA \ \ \

e - E x p t point

0 25 50 75 100

At % of Au - ~ -

Fig. 2. The variation of the resistivity of Au-Cu alloys with composition.

t h roughou t the composi t ion region where it is thermodynamical ly possible. It is seen that the order has a max imum effect at the critical composi t ions A u C u 3 and AuCu. The resistivities at these composi t ions are as low as for the pure elements.

(a) (b) Fig. 3. Electron diffraction patterns of gold-copper alloy films : (a) 50 at. % Au; (b) 65 at. % Au.

The periodicity of the lattice can thus be recovered to a large extent at these critical composit ions. Around these critical points where the composi t ion is non- stoichiometric the alloy is only partially ordered; large values o f the ratio Porder/Pdi~orO~r are usually at tr ibuted to the presence o f superstructures. Figure 3(a) and (b) shows electron diffraction patterns o f go ld-copper alloys with composi t ions of 50 at. % and 65 at. ~ Au respectively. Extra lines due to ordering are readily visible for a composi t ion o f 50 at. !Yoo Au. Figure 4(a) and (b) shows transmission electron micrographs o f the go ld-copper films; the smooth polycrystalline texture o f the films can be seen.

Au-Cu FILMS 109

(a) (b) Fig. 4. Transmission electron micrographs of Au-Cu films: (a) 50 a t .~ Au. 800 A (19130×): (b) 65 at. o/Au, 800 A (19130 x ).

Figure 5 shows the variation of the resistivity with temperature and the effect of thermal cycling on the resistivity of the films. It is apparent that the resistivity is proportional to the absolute temperature within the experimental temperature

E u

. c

2 5

2 0

10

35 i t % A ~ ~ : ) . l - - ' - - ' ~ t = 6 8 7 ~)

6 5 a t % ~ U o

~ t = 2000 A)

nt%~

20 =t % Au ~ ° - ~ - 7 , ° 2000 ~ ;

5 2 at "/. Au, ( t = 2OOO A )

~ 5 at % Au

__~9 ~ - - ( t = 2000 ~, >

t I i 0 5 0 i 0 0 150 200

T i n ° C p

Fig. 5. The variation of the resistivity of Au-Cu films with temperature, showing typical annealing and subsequent thermal cycling behaviour of a 687 ~, film (35 a t . ~ Au): O, experimental points; A, experimental points after annealing and subsequent thermal cycling.

110 A.K. PAL et al.

range 4. The results of annealing for 4 h and subsequent thermal cycling for a film (687 /~) of 35 at.'~/o Au are also shown in Fig. 5. It is observed that there is no annealing effect on the resistivity of the films and that the'p-Tplot retraces the same curve when the sample is subjected to thermal cycling.

oo

x u

"o

7

00

30

20

~0

t t

0

t

t \\

O

/ P S / \

/

/ /

J

I I

/ /

/

V

k \

t

"t ii I t t /

/ / /

\ \ / "

,t>~ /

/ / / / /

//

/ / /

0 25 50 75 100

At "/. of AU

Fig. 6. The plot of :~ vs. composition.

Figure 6 shows the typical variation of the temperature coefficient ~ of resistivity with composit ion for a film 2000 A thick. It was found that the ordered films had much higher values of c~ (about three to four times) than the disordered films.

It has been observed that the size effect is much more pronounced in films of disordered composit ion than in films with an ordered composit ion (Fig. 1). On the assumption that the free electron theory holds good for ordered composit ions in gold-copper alloys, the experimental data were compared with the equations TM 12

P 1 +3-(1 -p ) 7>1 (1)

and

p 4 1 - p 1 74 l , p < 1 (2)

Po 3 1 + pin(I /7)+0.4228

where p and Po are the resistivities of the film and bulk, respectively, for different ordered composit ions and 7 = t/l. The l andp values obtained from plots o f p versus l / t and P/Po versus ',, are shown in Table I.

A u - C u FILMS 1 1 1

The relations given in eqns. (1) and (2), when applied similarly to films having a disordered composi t ion, yielded the values o f / a n d p shown in Table II. The l values

thus obta ined for disordered alloys may not be the true values owing to the fact that the electrons cannot be treated as free electrons because of the mismatch in the phases in disordered alloys and therefore the Fuchs -Sondhe imer theory cannot be applied to these films.

TABLE I

Au (at. %) l (/~) p

52 310 0 50 306 0 25 340 0

TABLE II

Au (at.%) I(A) p

75 108.8 0 65 75 0 35 97 0

REFERENCES

1 C.H. Johansson and J. C. Linde, Ann. Phys. (Leipzig), 25 (1936) i, 2 T. Muto, Sci. Pap. lnst. Phys. Chem. Res. (Jpn), 30 (1936) 99. 3 T. Murakami, J. Phys. Soc. Jpn, 8 (1953) 453. 4 F.W. Jones and C. Sykes, Proc. R. Soc. London, Ser. A, 166 (1938) 376. 5 G.J. Dienes, J. Appl. Phys.,22(1951) 1020. 6 J.A. Brinkman, C. E. Dixon and C. J. Meeclan, Acta Metall., 2 (1954) 38. 7 R.A. Dugdale and A. Green, Philos. Mag., 45 (1954) 163. 8 D.W. Pashley and A. E. B. Presland, in C. A. Neugebauer, J. B. Newkirk and D. A. Vermilyea

(eds.), Structure and Properties o f Thin Films, Wiley, New York, 1959. 9 A .K . Pal, P. SenandA. K. Barua, ThinSolidFilms, 25(1975)S25.

10 L.J. vanderPauw, PhilipsRes. Rep.,13(1958) l. 11 E.H. Sondheimer, Adv. Phys., 1 (1952) 1. 12 R.G. Chambers, Proc. R. Soc. London, Ser. A, 202 (1950) 378.