Thin Solid Films, 74 (1980) 153-164 © Elsevier Sequoia S.A., Lausanne--Printed in the Netherlands 153

THE VARIATION IN ELECTRICAL RESISTANCE WITH TEMPERATURE FOR Bi/Ag BILAYER FILMS

JOY GEORGE AND E. C. JOY Department of Physics, University of Cochin, Cochin-682 022 (India) (Received March 27, 1980; accepted April 11, 1980)

The variation in the electrical resistance of vacuum-evaporated Bi/Ag bilayers with different layer thicknesses was studied as a function of temperature. A silver overlayer 50 A thick increased the variation in Rr/R with temperature of the bismuth film (R r is the resistance of the film at temperature T and R the resistance at room temperature). It increased the resistance of the film and made the temperature coefficient of resistance at room temperature more negative. In addition, the resistance minimum was shifted to higher temperatures. The variation in resistance with temperature is explained on the basis of the Kaidanov and Regal model. When the total thickness of the bilayer film was kept constant (approximately 1000 A), the variation in resistance on annealing was dependent on the thickness of the silver layer. The rapid rise in resistance above 100 °C observed in films with silver layers between 100 and 600 A thick is explained on the basis of diffusion at the interface and aggregation of the silver film on the surface. By controlling the thickness of the layers it is possible to keep the variation in resistance with temperature of the film to a minimum.

1. INTRODUCTION

Bismuth is a semimetal with many anomalies in its transport properties 1. The mean free path of the electrons in the metal at room temperature is of the order of some microns and hence the size effect can be observed in thicker samples even at room temperature. In bismuth the Fermi energy of the electrons is about 25 meV and the effective mass of the electrons along some crystal orientations is two or three orders of magnitude smaller than the free-electron mass 2. Therefore oscillations in the resistivity with variation in thickness having a period nearly equal to the de Broglie wavelength can be observed in bismuth films. Further, bismuth films in polycrystalline form are semiconducting and either n type or p type, and the nature of the films can be changed from one type to the other by varying the film thickness as well as the deposition parameters. Because of these anomalies the transport properties of thin bismuth films have been of interest for many years 3-6.

It has been observed by several investigators that the presence of an additional film layer, either as an electrode or as an overlayer, changes the properties of the original film7-~l. In bismuth films it has also been noticed that imperfections markedly alter the transport properties 12'13. Therefore in the present study the

154 J. GEORGE, E. C. JOY

influence of silver overlayers of various thicknesses on bismuth films was investigated (1) by depositing a silver overlayer of constant thickness on bismuth base layers of various thicknesses and (2) by varying the thickness of the individual layers of silver and bismuth while keeping the total thickness constant.

2. EXPERIMENTAL

The Bi/Ag bilayer films were prepared by sequential evaporation of bismuth and silver (both 99.999~ pure) from molybdenum boats in a vacuum of the order of 10-5 Torr. The films were deposited on microscope glass slides which had been cleaned chemically, ultrasonically and finally by ion bombardment in the vacuum chamber. In order to ensure that the layers were uniform in thickness the source-to- substrate distance was kept large (approximately 27 cm).

In the first part of the study the thickness of the bismuth film was varied from 1000 to 2000 A with the thickness of the silver overlayer kept constant (approximately 50 A). The width of the film was adjusted to 0.55 cm by using an appropriate mask during deposition. Electrical contacts were attached to the film to give an effective film length of 2 cm, and the samples were annealed at a temperature of 160 °C for more than 1 h in a vacuum of the order of 10 -4 Torr. They were heated radiantly through the back of the substrate. The temperature of the film was measured with a chromel-alumel thermocouple attached to the front of the film surface and with a voltage recorder of accuracy 0.2 mV cm- 1. After the specimen had been cooled to room temperature its resistance was measured in vacuum at different temperatures during both heating and cooling using a Marconi TF 2700 universal bridge. A study of the variation in resistance with temperature for pure bismuth films was also made for comparison.

In the second part of the investigation the total thickness of the bilayer films was kept constant (approximately 1000 A) and the thickness of the silver layer was varied. The films were heated in a vacuum of better than 10 -4 Torr and their resistances were measured at various temperatures during both heating and cooling. Before cooling, the films were kept at a temperature above 160 °C for more than 1 h. The films were also observed under reflected light in a metallurgical microscope. Certain annealed and unannealed samples exposed to an H2S atmosphere for 15 min were also examined in the microscope.

3. RESULTS

3.1. Bilayer films with a very thin silver overlayer The resistances of pure bismuth films and of films with a silver overlayer

approximately 50/k thick (all annealed at a temperature above 160 °C and then cooled to room temperature) were found to decrease on heating, to reach a minimum and then to increase with a further rise in temperature. This variation in resistance with temperature was found to be reversible. The variation in resistance with temperature as a plot of Rr /R against T is given in Fig. 1 (R is the resistance of the film at room temperature and R T its resistance at a temperature T). In these films the variation in resistance was found to decrease with an increase in the specimen thickness. In addition, the temperature corresponding to the resistance minimum also decreased with increasing thickness.

RKSISTANCE--TEMPERATURE CURVES FOR Bi /Ag FILMS 155

r-~

c ~

o,8

0'9

[ [ I I I I I I 40 8 0 t 2 0 160

(a) T (°E) (b)

0.9

C~

re'

0-8

' ~ ' ' do ' Jo ' ~ ' 160

T (t)

' ~o ' do ' Go ' t~o '

(0 T(t) Fig. 1. Variation in Rr/R with temperature for films of thickness (a) 1000 A, (b) 1500 A and (c) 2000 A: O, bismuth films; x, bilayer films.

5o

4 0

io

I I I

tooo '/~oo 200o

Fig. 2. Variation in room temperature sheet resistance with thickness: O, bismuth films; ×, bilayer films.

An overlayer of silver was found to modify the properties of the bismuth films. The resistance of b ismuth films with a silver overlayer approximately 50 A thick was found to be higher than that of pure bismuth films. The variat ion in the r o o m temperature sheet resistance with the thickness of the films is shown in Fig. 2. The

156 J . G E O R G E , E. C. JOY

specimens with silver overlayers had a larger variation in resistance with temperature than the pure bismuth films did, as is evident from Fig. 1. The temperature corresponding to the resistance minimum was also shifted to a higher temperature (Table I). Furthermore, the temperature coefficients of resistance (TCRs) of the films changed (Table II).

T A B L E I TEMPERATURE CORRESPONDING TO THE RESISTANCE MINIMUM OF FILMS WITH VARIOUS THICKNESSES

Thickness (A) Tmlnimu m (°C)

Bi film Bi film with Ag overlayer approximately 50/~ thick

1000 135 160

1500 100 110

2000 95 100

T A B L E II '

TEMPERATURE COEFFICIENT OF RESISTANCE AT ROOM TEMPERATURE FOR VARIOUS THICKNESSES OF

BISMUTH FILM WITH AND WITHOUT A SILVER OVERLAYER

Thickness (A) TCR ( p p m ° C - a) at room temperature

Bifilm Bismuthfilmwith Agoverlayerapproximately 50 ~ thick

1000 - 2 4 2 4 - 3 1 3 7

1500 - 2 8 4 2 - 3 0 0 9

2000 - 1474 - 2 7 3 2

The films were found to be n type. X-ray diffraction studies revealed that they were polycrystalline with no preferred orientation.

3.2. Bilayer films of constant thickness The variation in resistance with temperature of the specimens for various

thicknesses of the silver layer is shown in Fig. 3. In pure bismuth films and in bilayer films with a silver layer approximately 50 A thick the resistance decreases irreversibly with rise in temperature. After annealing at a temperature above 160 °C, the resistance was found to vary reversibly with temperature showing a resistance minimum (Figs. 3(a) and 3(b)). In films with silver layers 100 and 200 A thick the resistance on heating was found to decrease at first with a rise in temperature and then to increase slowly with a steep rise around 120°C followed by a gradual decrease above 150 °C. In films with silver layers 300-600 A thick the resistance initially increased slowly and then very rapidly; finally it decreased slowly. The magnitude of the variation in resistance decreased with increase in the thickness of the silver layer. On cooling, the resistance was found to increase in all these cases and the variation in resistance appeared to depend on the thickness of the individual layers. On further heating and cooling, the resistance variation followed the original cooling curve. For a film with a layer 600 A thick the value of the resistance after the first heating remained almost steady during further heating and cooling. When the

RESISTANCE-TEMPERATURE CURVES FOR Bi/Ag FILMS 157

420

I00

4.o I 0 2o (a)

14-c

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(b) 0

180

14c

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(c)

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T {" ° c )

I I I I I

4o 80 (°C)

i i , i i I

40 80 120 T { ~ 1

i i

160

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f ~ 12©

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(d) T (~)

158 J. GEORGE, E. C. JOY

t 2 0

9 0 ¸

60

3O

(e)

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T( 'c)

t 0 0

, ¢

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(f)

i , i , t , i 40 go ~2o 16o

"~ ('c)

RESISTANCE--TEMPERATURE CURVES FOR B i / A g FILMS 159

"/o-

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(g)

4.0,

20 1¢

0 0

(h)

.'Io

0 0

(i)

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T ( ° c )

I 2 0 0

f :ZOO

200

° I I I I i i i I I I

0 40 80 120 ~60 ~'00

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Fig. 3. Variation in resistance with temperature for bilayer films of constant thickness with silver overlayer thicknesses of (a) 0 A, (b) 50 A, (c) 100 A, (d) 150 A, (e) 200 A. (f) 300 A, (g) 400 A, (h) 500 A, (i) 600 A and (j) 700 A.

160 J . GEORGE, E. C. J O Y

silver layer was thicker than 600 A, the resistance of the films slowly increased with rise in temperature, showing a positive TCR during both heating and cooling.

The variation in the room temperature sheet resistance of the films with the thickness of the silver layer before and after heat treatment is shown in Fig. 4. The TCRs for various thicknesses of silver are given in Table III. The values showed a marked difference between the films with overlayers 50 A thick and those with

5O

30 J

o, tgo ' 3~o ' 5bo ' ~6o v ~ o

^4 Lax°, T ick.,s Fig. 4. Plots of the sheet resistance of bilayer films against the silver layer thickness: O, before heat treatment; x , after heat treatment.

T A B L E I I I

TEMPERATURE COEFFICIENT OF RESISTANCE AT ROOM TEMPERATURE FOR VARIOUS THICKNESSES OF THE

SILVER LAYER

Ag layer thickness (A) o 1 TCR ( p p m C - ) at room temperature

First heating Further heating

0 - -4050 - -2130

50 -- 3580 -- 2100

100 -- 1680 - 4220

150 - 1180 - -3800

200 -- 770 -- 3740

300 + 190 - 3220

400 + 410 - 3080

500 + 500 - 2760

600 + 630 -- 170

700 + 750 + 885

800 + 790 + 1020

900 + 1020 + 1060

RESISTANCE--TEMPERATURE CURVES FOR Bi/Ag FILMS 161

overlayers 100 A thick. As the thickness of the silver layer was increased, the TCR at room temperature slowly changed from a negative to a positive value.

When identical specimens were annealed in vacuum at various constant temperatures (1"00, 120 and 140 °C) the time taken to reach the maximum value of the resistance decreased with the rise in temperature. Although at 100 °C a specimen took several hours to reach the maximum value of resistance, at 120 °C it took only about 2 h and at 140 °C only a few minutes.

Freshly prepared samples with thinner overlayers showed no special surface features when examined under the microscope. When the films were annealed at 160 °C and then exposed to an H2S atmosphere for 15 min they were found to have dispersed dark regions on the surface. These features were absent in unannealed films exposed to H2S (Fig. 5).

(a) (b) Fig. 5. Surfa•ef•atures•faBi/Agbi•ay•r••m(th•si•ver•ayerisappr•ximate•y2••Athi¢k)exp•sedt•an H2S atmosphere: (a) unannealed; (b) annealed. (Magnification, 940 x .)

4. DISCUSSION

4.1. Films with a silver overlayer 50 ~ thick Comparing Fig. 3(b) with Figs. 3(a) and 3(c)-3(i) it can be seen that the

behaviour of a bismuth film with a silver overlayer approximately 50 A thick is similar to that of a pure bismuth film. This may be because the silver does not form a continuous overlayer on the bismuth and therefore does not contribute directly to the conduction. In addition the TCR at room temperature for different silver layer thicknesses (Table III) and the variation in sheet resistance before annealing with silver layer thickness (Fig. 4) indicate that the behaviour of a film with a silver overlayer 50 A thick is different from that of films with thicker silver layers.

The variation in resistance with temperature (the resistance showing a minimum at a particular temperature and then increasing with further heating or cooling) for bismuth and for Bi/Ag bilayer films can be explained as a consequence of a limitation in the mean free path and of changes in the number of charge carriers, as suggested by Hoffman and Frank112 and Block and Gaddy 13 for bismuth films using the model proposed by Kaidanov and Regal ~4. According to their model, at temperatures above the resistance minimum the mean free path of the charge carriers is smaller than the crystallite size. As the temperature decreases, the mean free path increases rapidly and the density of carriers decreases. However, the

162 J. GEORGE, E.C. JOY

increase in the mean free path overrides the decrease in the density of carriers and so the overall resistance decreases. Once the mean free path becomes comparable with the crystallite size, it increases very slowly with decrease in temperature until finally a temperature is reached at which the rate of increase in the mean free path becomes slower than the decrease in the charge carrier density. On further decrease in temperature the net effect is an increase in the resistance. It has also been pointed out by Hoffman and Frankl 12 that the semiconductor-like behaviour observed in thin bismuth films is a consequence of the limitation in the carrier mean free path and of the decrease in the number of carriers with decreasing temperature rather than of the uncrossing of the conduction and valence bands, as predicted by the quantum size effect theory and suggested by Duggal and Rup 15.

It has been shown by several investigators that the deposition of an overlayer of one material modifies the surface of the underlayer and consequently the electrical properties of this layer 16. This modification at the surface, which depends on the combination of the layers, influences the scattering of electrons and the effective number of free electrons near the interface. Depending on the nature of the change, an increase or decrease in the surface scattering may occur~ The resistance of a bismuth film with a silver overlayer approximately 50 A thick was found to be higher than that of a pure bismuth film of the same thickness (Fig. 2). Therefore it may reasonably be assumed that the silver layer which is present on the bismuth base layer modifies the interface so as to increase the surface scattering of electrons and hence the resistivity of the film.

The slower rate of variation in resistance and the shift in the resistance minimum to a lower temperature region, which were observed as the thicknesses of the bismuth and the Bi/Ag bilayer films increased, are caused by the increasing crystallite size with increasing film thickness, as observed by Neuman and Ko 17 in bismuth films. The shift in the resistance minimum to a higher temperature for bismuth films with a thin silver overlayer compared with pure bismuth films of the same thickness may be due to the decrease in the mean free path which arises from the increase in the surface scattering of electrons resulting from the modification of the interface by the silver layer.

4.2. Films with various layer thicknesses Since the resistance of a thin metal film reflects the microstructure of the film 1 s

to a remarkable degree, the variation in resistance in the bilayer films demonstrates the changes occurring in them.

Depending on the thickness of the silver layer, we found a slow decrease or a gradual increase in resistance during the initial stages of beating. This change may be partly caused by the slight interdiffusion of the materials which is possible in this temperature range, but the main reason appears to be the combined effect of the resistance changes occurring in the individual layers. As the thickness of the silver layer is increased, the variation in the effective resistance increases because the material has a positive TCR.

The steep increase in resistance occurring in the films above 100 °C appears to be caused by increased interdiffusion at that temperature and aggregation in the overlayer.

As grain boundaries play a major role in the process of diffusion in

RESISTANCE--TEMPERATURE CURVES FOR Bi/Ag FILMS 163

polycrystalline films 19, the motion of material in double-layer films is pre- dominantly from the layer with a smaller number of grains rather than from the layer with a larger number of grains 2°. If the melting point of a material is high, the size of the grains in its polycrystalline film form is small and hence the number of grains is large 21. Therefore, as the melting point of silver is higher than that of bismuth, there is a larger number of grains in the upper silver layer and so diffusion of bismuth into the silver is possible. Such a diffusion of bismuth into gold has already been observed by Pariset and Chauvineau 22. In pairs of materials such as Cr/Cu and Au/Ni, which have very little mutual solubility (less than 0.1~o) and no compound formation, intermixing has been observed at higher temperatures when the metals are in the form of polycrystaUine double layers19.20. In a similar manner, good intermixing is also possible in Bi/Ag polycrystalline bilayers for which the solid solubility of bismuth in silver is 3 at.~o and that of silver in bismuth is negligible 23. The diffusion of bismuth into the silver layer increases the resistance of the bilayer as for Cr/Au bilayers where the resistance has been observed to increase because of chromium diffusion into the gold 24.

Interdiffusion and intermixing in multilayer films are found to increase with a rise in temperature. In Bi/Ag films the diffusion appears to be rapid above 100 °C which is a temperature of the order of 2Tm where Tm is the melting point of the metal. The increasing rate of diffusion with temperature is evident from the length of time taken to reach the maximum value of resistance when the specimens were annealed at 100, 120 and 140 °C.

Belser is has shown that in two-layer films there may be a sharp increase in resistance, which in many cases is due to compound formation and in some cases is due to aggregation of one of the metals. Microscope observation of the annealed samples with thinner silver overlayers after H2S treatment seems to indicate the occurrence of aggregation of silver in these samples (Fig. 5(b)). According to Weaver 25 the aggregation generally occurs at a high temperature which for silver is about 300 °C. Hollingsworth Smith and Gurev 26 have also shown that severe agglomeration occurs at temperatures greater than 200 °C in the presence of oxygen. Mohan and Jayarama Reddy's 27 study, however, shows that agglomeration occurs in thin silver films around 160 °C. In Bi/Ag bilayers, diffusion of the bismuth may have assisted the occurrence of aggregation at a lower temperature.

From the above considerations it is suggested that the steep rise in resistance observed above 100 °C is caused by the diffusion of bismuth into the silver overlayer and aggregation of the overlayer film.

The final slow decrease in resistance above 150°C is due to the gradual annealing-out of defects. The behaviour of the film after the first annealing appears to depend on the ratio of bismuth to silver in the films.

The components of the bilayer film do not have a normal compound phase. Since they retain their individual properties, as the quantity of silver increases the properties of the films are dominated more and more by the silver. In films with a silver layer 600 A thick the decrease in the resistance of bismuth after annealing is balanced by the increase in the resistance of silver, so a steady value of resistance is observed in the film, at least for a certain range of temperature. When the silver layer is thicker than 600 A there is a slow increase in resistance with an increase in temperature due to the positive TCR of the dominating silver part.

164 J. GEORGE, E.C. JOY

5. CONCLUSIONS

A thin overlayer of silver (approximately 50 A thick) modifies the properties of bismuth underlayers. It increases the resistivity and makes the TCR of the bismuth film more negative at room temperature. It also shifts the resistance minimum to a higher temperature. When the thickness of the bilayer is kept constant, the electrical properties depend on the thickness of the individual layers. The sheet resistance of films in which the silver layer is thicker than 100 A decreases with an increase in the thickness of the silver layer. The TCR at room temperature also changes from negative to positive values. By controlling the thickness of the layers, it is possible to keep the variation in resistance with temperature to a minimum.

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